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Galaktionov, Victor Aleksandrovich

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Author ID: galaktionov.victor-a Recent zbMATH articles by "Galaktionov, Victor Aleksandrovich"
Published as: Galaktinov, Victor A.; Galaktionov, V. A.; Galaktionov, Victor; Galaktionov, Victor A.
Homepage: http://www.maths.bath.ac.uk/~vag/
External Links: MGP · Math-Net.Ru · dblp · GND
Documents Indexed: 251 Publications since 1979, including 10 Books
all top 5

Serials

15 Differential Equations
15 U.S.S.R. Computational Mathematics and Mathematical Physics
13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
11 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
11 Soviet Mathematics. Doklady
9 Advances in Differential Equations
8 European Journal of Applied Mathematics
8 Differential and Integral Equations
8 Mathematics of the USSR, Sbornik
7 Nonlinearity
6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
6 Studies in Applied Mathematics
6 Advanced Nonlinear Studies
5 SIAM Journal on Mathematical Analysis
4 Journal of Differential Equations
4 Computational Mathematics and Mathematical Physics
4 Communications in Partial Differential Equations
4 Soviet Physics. Doklady
4 Communications in Contemporary Mathematics
3 Archive for Rational Mechanics and Analysis
3 SIAM Journal on Applied Mathematics
3 NoDEA. Nonlinear Differential Equations and Applications
3 Discrete and Continuous Dynamical Systems
3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
3 Matematicheskoe Modelirovanie
3 Nonlinear Analysis. Theory, Methods & Applications
2 IMA Journal of Applied Mathematics
2 Journal of Mathematical Analysis and Applications
2 Journal of Mathematical Physics
2 Mathematical Notes
2 Differentsial’nye Uravneniya
2 Indiana University Mathematics Journal
2 Journal of Computational and Applied Mathematics
2 Journal of Functional Analysis
2 Physica D
2 Asymptotic Analysis
2 Journal of Partial Differential Equations
2 Journal of Mathematical Sciences (New York)
2 Doklady Mathematics
2 Nonlinear Analysis. Real World Applications
2 Proceedings of the Steklov Institute of Mathematics
1 Communications on Pure and Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Engineering Mathematics
1 Mathematical Methods in the Applied Sciences
1 Rocky Mountain Journal of Mathematics
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of the London Mathematical Society. Second Series
1 Journal of Soviet Mathematics
1 Matematicheskiĭ Sbornik. Novaya Seriya
1 Mathematische Annalen
1 Quarterly of Applied Mathematics
1 Transactions of the American Mathematical Society
1 Revista Matemática de la Universidad Complutense de Madrid
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Electronic Journal of Differential Equations (EJDE)
1 Georgian Mathematical Journal
1 Journal of Mathematical Sciences. University of Tokyo
1 Sbornik: Mathematics
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 Interfaces and Free Boundaries
1 Journal of the European Mathematical Society (JEMS)
1 Journal of Nonlinear Mathematical Physics
1 Journal of Evolution Equations
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Communications on Pure and Applied Analysis
1 Analysis and Applications (Singapore)
1 Mediterranean Journal of Mathematics
1 Boundary Value Problems
1 De Gruyter Expositions in Mathematics
1 Progress in Nonlinear Differential Equations and Their Applications
1 Monographs and Research Notes in Mathematics

Publications by Year

Citations contained in zbMATH

195 Publications have been cited 2,582 times in 1,316 Documents Cited by Year
Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld. Zbl 1020.35001
Samarskii, A. A.; Galaktionov, V. A.; Kurdyumov, S. P.; Mikhailov, A. P.
284
1995
Continuation of blowup solutions of nonlinear heat equations in several space dimensions. Zbl 0874.35057
Galaktionov, Victor A.; Vazquez, Juan L.
136
1997
The problem of blow-up in nonlinear parabolic equations. Zbl 1010.35057
Galaktionov, Victor A.; Vázquez, Juan L.
134
2002
Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics. Zbl 1153.35001
Galaktionov, Victor A.; Svirshchevskii, Sergey R.
93
2007
A general approach to critical Fujita exponents in nonlinear parabolic problems. Zbl 1139.35317
Galaktionov, Victor A.; Levine, Howard A.
78
1998
On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary. Zbl 0851.35067
Galaktionov, Victor A.; Levine, Howard A.
70
1996
Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities. Zbl 0824.35128
Galaktionov, Victor A.
58
1995
Blow-up for quasilinear heat equations with critical Fujita’s exponents. Zbl 0808.35053
Galaktionov, Victor A.
58
1994
Geometric Sturmian theory of nonlinear parabolic equations and applications. Zbl 1075.35017
Galaktionov, Victor A.
43
2004
On new exact blow-up solutions for nonlinear heat conduction equations with source and applications. Zbl 0735.35074
Galaktionov, Victor A.
40
1990
On a parabolic system of quasilinear equations. I. Zbl 0556.35071
Galaktionov, V. A.; Kurdyumov, S. P.; Samarskij, A. A.
38
1983
Existence and blow up for higher-order semilinear parabolic equations: majorizing order-preserving operators. Zbl 1082.35079
Galaktionov, V. A.; Pohozaev, S. I.
36
2002
A parabolic system of quasilinear equations. II. Zbl 0599.35085
Galaktionov, V. A.; Kurdyumov, S. P.; Samarskij, A. A.
36
1985
Asymptotic behaviour of nonlinear parabolic equations with critical exponents. A dynamical systems approach. Zbl 0755.35010
Galaktionov, Victor A.; Vazquez, Juan L.
35
1991
On asymptotic self-similar behaviour for a quasilinear heat equation: Single point blow-up. Zbl 0828.35067
Galaktionov, Victor A.
34
1995
On asymptotic ”eigenfunctions” of the Cauchy problem for a nonlinear parabolic equation. Zbl 0607.35049
Galaktionov, V. A.; Kurdyumov, S. P.; Samarskij, A. A.
33
1986
Blow-up and critical exponents for nonlinear hyperbolic equations. Zbl 1012.35058
Galaktionov, V. A.; Pohozaev, S. I.
32
2003
Third-order nonlinear dispersive equations: shocks, rarefaction, and blowup waves. Zbl 1177.76183
Galaktionov, V. A.; Pokhozhaev, S. I.
31
2008
A quasilinar heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures. Zbl 0699.35134
Galaktionov, V. A.; Dorodnitsyn, V. A.; Elenin, G. G.; Kurdyumov, S. P.; Samarskij, A. A.
31
1986
Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations. Zbl 0827.35055
Galaktionov, Victor A.; Vazquez, Juan L.
30
1995
Global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1122.35040
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
29
2004
Rate of approach to a singular steady state in quasilinear reaction-diffusion equations. Zbl 0920.35080
Dold, James W.; Galaktionov, Victor A.; Lacey, Andrew A.; Vázquez, Juan Luis
29
1998
Self-similar blow-up in higher-order semilinear parabolic equations. Zbl 1112.35095
Budd, C. J.; Galaktionov, V. A.; Williams, J. F.
26
2004
Quasilinear heat equations with first-order sign-invariants and new explicit solutions. Zbl 0817.35037
Galaktionov, Victor A.
24
1994
Unstable sixth-order thin film equation. I: Blow-up similarity solutions. Zbl 1173.35562
Evans, J. D.; Galaktionov, V. A.; King, J. R.
23
2007
Extinction for a quasilinear heat equation with absorption. I: Technique of intersection comparison. Zbl 0831.35073
Galaktionov, Victor A.; Vazquez, Juan L.
23
1994
Source-type solutions of the fourth-order unstable thin film equation. Zbl 1156.35387
Evans, J. D.; Galaktionov, V. A.; King, J. R.
22
2007
Extinction for a quasilinear heat equation with absorption. II: A dynamical systems approach. Zbl 0831.35074
Galaktionov, Victor A.; Vazquez, Juan L.
22
1994
Peaking modes in problems for quasilinear parabolic equations. (Rezhimy s obostreniem v zadachakh dlya kvazilinejnykh parabolicheskikh uravnenij). Zbl 0631.35002
Samarskij, A. A.; Galaktionov, V. A.; Kurdyumov, S. P.; Mikhajlov, A. P.
22
1987
Unstable sixth-order thin film equation. II: Global similarity patterns. Zbl 1173.35530
Evans, J. D.; Galaktionov, V. A.; King, J. R.
21
2007
On very singular similarity solutions of a higher-order semilinear parabolic equation. Zbl 1063.35077
Galaktionov, V. A.; Williams, J. F.
21
2004
A stability technique for evolution partial differential equations. A dynamical systems approach. Zbl 1065.35002
Galaktionov, Victor A.; Vázquez, Juan Luis
21
2004
On a certain boundary value problem for the non-linear parabolic equation \(u_ t=\Delta u^ (\sigma+1)+u^\beta\). Zbl 0468.35056
Galaktionov, V. A.
21
1981
Unbounded solutions of the Cauchy problem for the parabolic equation \(u_t=\nabla(u^{\alpha\nabla u})+u^\beta\). Zbl 0515.35045
Galaktionov, V. A.; Kurdyumov, S. P.; Mikhajlov, A. P.; Samarskij, A. A.
21
1980
On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations. Zbl 1176.35094
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
20
2009
On the necessary conditions of global existence to a quasilinear inequality in the half-space. Zbl 0943.35110
Egorov, Yuri V.; Galaktionov, Victor A.; Kondratiev, Vladimir A.; Pohozaev, Stanislav I.
20
2000
Blow-up for quasilinear heat equations described by means of nonlinear Hamilton-Jacobi equations. Zbl 0884.35014
Galaktionov, Victor A.; Vazquez, Juan L.
19
1996
Asymptotics of the fast-diffusion equation with critical exponent. Zbl 0954.35094
Galaktionov, Victor A.; Peletier, Lambertus A.; Vazquez, Juan L.
18
2000
New explicit solutions of quasilinear heat equations with general first-order sign-invariants. Zbl 0884.35056
Galaktionov, Victor A.; Posashkov, Sergey A.
18
1996
Application of new comparison theorem in the investigation of unbounded solutions of nonlinear parabolic equations. Zbl 0632.35028
Galaktionov, V. A.; Posashkov, S. A.
18
1986
Asymptotic behaviour near finite-time extinction for the fast diffusion equation. Zbl 0885.35058
Galaktionov, Victor A.; Peletier, Lambertus A.
17
1997
Regional blow up in a semilinear heat equation with convergence to a Hamilton-Jacobi equation. Zbl 0813.35033
Galaktionov, Victor A.; Vazquez, Juan L.
17
1993
Blow-up similarity solutions of the fourth-order unstable thin film equation. Zbl 1221.35296
Evans, J. D.; Galaktionov, V. A.; King, J. R.
16
2007
Blow-up and global asymptotics of the limit unstable Cahn-Hilliard equation. Zbl 1110.35023
Evans, J. D.; Galaktionov, V. A.; Williams, J. F.
16
2006
Single point blow-up for \(n\)-dimensional quasilinear equations with gradient diffusion and source. Zbl 0767.35033
Galaktionov, Victor A.; Posashkov, Sergey A.
16
1991
Saint-Venant’s principle in blow-up for higher-order quasilinear parabolic equations. Zbl 1064.35068
Galaktionov, V. A.; Shishkov, A. E.
15
2003
Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations. Zbl 1320.35002
Galaktionov, Victor A.; Mitidieri, Enzo L.; Pohozaev, Stanislav I.
13
2015
Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators. Zbl 1109.35015
Galaktionov, V. A.; Pohozaev, S. I.
13
2006
Singularities for a 2-dimensional semilinear elliptic equation with a non-Lipschitz nonlinearity. Zbl 0927.35037
Bidaut-Véron, Marie-Françoise; Galaktionov, Victor; Grillot, Philippe; Véron, Laurent
13
1999
Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations. Zbl 0842.35006
Galaktionov, Victor A.; Vazquez, Juan Luis
13
1995
On a blow-up set for the quasilinear heat equation \(u_ t=(u^ \sigma u_ x)_ x + u^{\sigma+1}\). Zbl 0802.35065
Galaktionov, Victor A.
13
1993
On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach. Zbl 1219.35123
Galaktionov, V. A.
12
2009
Intermediate asymptotics for inhomogeneous nonlinear heat conduction. Zbl 1205.35146
Galaktionov, V. A.; Kamin, S.; Kersner, R.; Vazquez, J. L.
12
2003
On a spectrum of blow-up patterns for a higher-order semilinear parabolic equation. Zbl 0995.35009
Galaktionov, Victor A.
12
2001
An asymptotic and numerical description of self-similar blow-up in quasilinear parabolic equations. Zbl 0932.65099
Budd, C. J.; Collins, G. J.; Galaktionov, V. A.
12
1998
Stability and spectra of blow-up in problems with quasi-linear gradient diffusivity. Zbl 1023.35053
Budd, Chris; Galaktionov, Victor
12
1998
Generalized separation of variables for differential equations with polynomial nonlinearities. Zbl 0855.35028
Galaktionov, V. A.; Posashkov, S. A.; Svirshchevskij, S. R.
12
1995
Conditions for global non-existence and localizations of solutions of the Cauchy problem for a class of non-linear parabolic equations. Zbl 0576.35055
Galaktionov, V. A.
12
1983
Boundary-value problem for the nonlinear parabolic equation \(u_ t\) = Delta u**(sigma+1) + u**beta. Zbl 0478.35058
Galaktionov, V. A.
12
1981
On nonexistence of Baras-Goldstein type for higher-order parabolic equations with singular potentials. Zbl 1211.35161
Galaktionov, V. A.; Kamotski, I. V.
11
2010
Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach. Zbl 1197.35062
Galaktionov, V. A.
11
2009
Non-uniqueness and global similarity solutions for a higher-order semilinear parabolic equation. Zbl 1067.35032
Galaktionov, V. A.; Harwin, P. J.
11
2005
Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents. Zbl 1019.35042
Galaktionov, Victor A.; King, John R.
11
2003
Regularity of interfaces in diffusion processes under the influence of strong absorption. Zbl 0938.35082
Galaktionov, Victor A.; Shmarev, S. I.; Vazquez, Juan L.
11
1999
Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches. Zbl 1320.35174
Álvarez-Caudevilla, Pablo; Galaktionov, Victor A.
10
2015
Local bifurcation-branching analysis of global and “blow-up” patterns for a fourth-order thin film equation. Zbl 1298.35104
Álvarez-Caudevilla, P.; Galaktionov, V. A.
10
2011
Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem. Zbl 0896.35143
Galaktionov, Victor A.; Hulshof, Josephus; Vazquez, Juan L.
10
1997
On new exact solutions of parabolic equations with quadratic nonlinearities. Zbl 0695.35096
Galaktionov, V. A.; Posashkov, S. A.
10
1989
Proof of the localization of unbounded solutions of the nonlinear parabolic equation \(u_ t=(u^{\sigma}u_ x)_ x+u^{\beta}\). Zbl 0573.35047
Galaktionov, V. A.
10
1985
Higher-order quasilinear parabolic equations with singular initial data. Zbl 1154.35374
Galaktionov, V. A.; Shishkov, A. E.
9
2006
On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1020.35029
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
9
2002
Fast diffusion equation with critical Sobolev exponent in a ball. Zbl 0988.35088
Galaktionov, Victor A.; King, John R.
9
2002
Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II. Zbl 1244.35019
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
8
2011
Groups of scalings and invariant sets for higher-order nonlinear evolution equations. Zbl 1161.35425
Galaktionov, Victor A.
8
2001
Regional blow-up for a higher-order semilinear parabolic equation. Zbl 1002.35061
Chaves, Manuela; Galaktionov, Victor A.
8
2001
Ordered invariant sets for KdV-type nonlinear evolution equations. Zbl 0972.35120
Galaktionov, V. A.
8
1999
Maximal sign-invariants of quasilinear parabolic equations with gradient diffusivity. Zbl 0933.35093
Galaktionov, Victor A.; Posashkov, Sergey A.
8
1998
Focusing blow-up for quasilinear parabolic equations. Zbl 0917.35061
Budd, C. J.; Galaktionov, V. A.; Chen, Jianping
8
1998
On classification of blow-up patterns for a quasilinear heat equation. Zbl 0851.35057
Bebernes, J.; Galaktionov, Victor A.
8
1996
Asymptotics of blowup for weakly quasilinear parabolic problems. Zbl 0812.35010
Bebernes, J.; Bricher, S.; Galaktionov, V. A.
8
1994
The space structure near a blow-up point for semilinear heat equations: A formal approach. Zbl 0747.35014
Velázques, J. J. L.; Galaktionov, V. A.; Herrero, M. A.
8
1991
New exact solutions of parabolic equations with quadratic nonlinearities. Zbl 0711.35063
Galaktionov, V. A.; Posashkov, S. A.
8
1989
A nonlinear elliptic problem with a complex spectrum of solutions. Zbl 0619.35043
Galaktionov, V. A.; Kurdyumov, S. P.; Posashkov, S. A.; Samarskij, A. A.
8
1986
Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range: second-order diffusion. Zbl 1298.35020
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
7
2014
Evolution completeness of separable solutions of nonlinear diffusion equations in bounded domains. Zbl 1065.35157
Galaktionov, V. A.
7
2004
On similarity solutions and blow-up spectra for a semilinear wave equation. Zbl 1039.35066
Galaktionov, V. A.; Pohozaev, S. I.
7
2003
Critical global asymptotics in higher-order semilinear parabolic equations. Zbl 1035.35048
Galaktionov, Victor A.
7
2003
On the behaviour of blow-up interfaces for an inhomogeneous filtration equation. Zbl 0869.35076
Galaktionov, V. A.; King, J. R.
7
1996
Asymptotics of unbounded solutions of the nonlinear equation \(u_ t=(u^{\sigma}u_ x)_ x+u^{\beta}\) near a “singular” point. Zbl 0629.35061
Galaktionov, V. A.
7
1986
The conditions for there to be no global solutions of a class of quasilinear parabolic equations. Zbl 0548.35068
Galaktionov, V. A.
7
1982
Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations. Zbl 1317.35061
Álvarez-Caudevilla, P.; Colorado, E.; Galaktionov, V. A.
6
2015
Shock waves and compactons for fifth-order non-linear dispersion equations. Zbl 1218.35002
Galaktionov, Victor A.
6
2010
Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation. Zbl 1152.35101
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
6
2008
Uniqueness of asymptotic profiles for an extinction problem. Zbl 1290.35141
Ferreira, R.; Galaktionov, V. A.; Vazquez, J. L.
6
2002
Second-order interface equations for nonlinear diffusion with very strong absorption. Zbl 0973.35096
Galaktionov, Victor A.; Shmarev, Sergei I.; Vazquez, Juan L.
6
1999
Best possible upper bound for blow-up solutions of the quasilinear heat conduction equation with source. Zbl 0771.35026
Galaktionov, Victor A.
6
1991
Any large solution of a nonlinear heat conduction equation becomes monotonic in time. Zbl 0741.35004
Galaktinov, Victor A.; Posashkov, Sergey A.
6
1991
Asymptotic behavior of unbounded solutions of the nonlinear parabolic equation \(u_ t=(u^{\sigma}\,u_ x)_ x+u^{\sigma +1}\). Zbl 0615.35048
Galaktionov, V. A.
6
1985
On localization conditions for unbounded solutions of quasilinear parabolic equations. Zbl 0506.35012
Galaktionov, V. A.
6
1982
On conditions for nonexistence of global solutions of a certain class of quasilinear parabolic equations. Zbl 0501.35043
Galaktionov, V. A.
6
1982
Countable families of solutions of a limit stationary semilinear fourth-order Cahn-Hilliard-type equation. I: Mountain pass and Lusternik-Schnirel’man patterns in \(\mathbb{R}^{N}\). Zbl 1352.35031
Álvarez-Caudevilla, P.; Evans, J. D.; Galaktionov, V. A.
3
2016
Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations. Zbl 1320.35002
Galaktionov, Victor A.; Mitidieri, Enzo L.; Pohozaev, Stanislav I.
13
2015
Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches. Zbl 1320.35174
Álvarez-Caudevilla, Pablo; Galaktionov, Victor A.
10
2015
Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations. Zbl 1317.35061
Álvarez-Caudevilla, P.; Colorado, E.; Galaktionov, V. A.
6
2015
The Cauchy problem for a tenth-order thin film equation. II: Oscillatory source-type and fundamental similarity solutions. Zbl 06376336
Álvarez-Caudevilla, P.; Evans, J. D.; Galaktionov, V. A.
2
2015
Global blow-up for a semilinear heat equation on a subspace. Zbl 1335.35134
Budd, C. J.; Dold, J. W.; Galaktionov, V. A.
1
2015
Towards optimal regularity for the fourth-order thin film equation in \(\mathbb R^N\): Graveleau-type focusing self-similarity. Zbl 1322.35051
Álvarez-Caudevilla, P.; Evans, J. D.; Galaktionov, V. A.
1
2015
Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation. Zbl 1433.35165
Alvarez-Caudevilla, Pablo; Galaktionov, Victor A.
1
2015
The \(p\)-Laplace equation in domains with multiple crack section via pencil operators. Zbl 1312.35117
Álvarez-Caudevilla, Pablo; Galaktionov, Victor A.
1
2015
Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range: second-order diffusion. Zbl 1298.35020
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
7
2014
On self-similar blow-up in evolution equations of Monge-Ampère type. Zbl 1267.35045
Budd, C. J.; Galaktionov, V. A.
3
2013
The KPP-problem and \(\log t\)-front shift for higher-order semilinear parabolic equations. Zbl 1295.35003
Galaktionov, V. A.
1
2013
The Cauchy problem for a tenth-order thin film equation. I. bifurcation of oscillatory fundamental solutions. Zbl 1308.35027
Álvarez-Caudevilla, Pablo; Evans, Jonathan D.; Galaktionov, Victor A.
1
2013
Steady states, global existence and blow-up for fourth-order semilinear parabolic equations of Cahn-Hilliard type. Zbl 1280.35067
Álvarez-Caudevilla, Pablo; Galaktionov, Victor A.
4
2012
Global sign-changing solutions of a higher order semilinear heat equation in the subcritical Fujita range. Zbl 1388.35076
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozhaev, Stanislav I.
1
2012
Eigenfunctions and very singular similarity solutions of odd-order nonlinear dispersion PDEs: toward a “nonlinear Airy function” and others. Zbl 1260.35099
Fernandes, R. S.; Galaktionov, V. A.
1
2012
Local bifurcation-branching analysis of global and “blow-up” patterns for a fourth-order thin film equation. Zbl 1298.35104
Álvarez-Caudevilla, P.; Galaktionov, V. A.
10
2011
Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II. Zbl 1244.35019
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
8
2011
Very singular similarity solutions and Hermitian spectral theory for semilinear odd-order PDEs. Zbl 1249.35146
Fernandes, R. S.; Galaktionov, V. A.
5
2011
Single point gradient blow-up and nonuniqueness for a third-order nonlinear dispersion equation. Zbl 1213.35252
Galaktionov, Victor A.
4
2011
Invariant solutions of nonlinear diffusion equations with maximal symmetry algebra. Zbl 1362.35018
Galaktionov, V. A.; Svirshchevskii, S. R.
3
2011
Boundary characteristic point regularity for semilinear reaction-diffusion equations: towards an ODE criterion. Zbl 1286.35123
Galaktionov, V. A.; Maz’ya, V.
2
2011
On continuous branches of very singular similarity solutions of the stable thin film equation. II: Free-boundary problems. Zbl 1227.35148
Evans, J. D.; Galaktionov, V. A.
1
2011
On continuous branches of very singular similarity solutions of a stable thin film equation. I: The Cauchy problem. Zbl 1227.35147
Evans, J. D.; Galaktionov, V. A.
1
2011
On nonexistence of Baras-Goldstein type for higher-order parabolic equations with singular potentials. Zbl 1211.35161
Galaktionov, V. A.; Kamotski, I. V.
11
2010
Shock waves and compactons for fifth-order non-linear dispersion equations. Zbl 1218.35002
Galaktionov, Victor A.
6
2010
Incomplete self-similar blow-up in a semilinear fourth-order reaction-diffusion equation. Zbl 1196.35058
Galaktionov, V. A.
4
2010
On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation. I: Local oscillatory properties. Zbl 1187.35122
Chaves, M.; Galaktionov, V. A.
4
2010
Very singular solutions for thin film equations with absorption. Zbl 1333.35117
Galaktionov, V. A.
4
2010
On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations. Zbl 1176.35094
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
20
2009
On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach. Zbl 1219.35123
Galaktionov, V. A.
12
2009
Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach. Zbl 1197.35062
Galaktionov, V. A.
11
2009
On center subspace behavior in thin film equations. Zbl 1196.35128
Galaktionov, V. A.; Harwin, P. J.
5
2009
Variational approach to complicated similarity solutions of higher order nonlinear evolution partial differential equations. Zbl 1179.35074
Galaktionov, Victor; Mitidieri, Enzo; Pokhozhaev, Stanislav
4
2009
The formation of shocks and fundamental solution of a fourth-order quasilinear Boussinesq-type equation. Zbl 1169.35361
Galaktionov, Victor A.
3
2009
On \(\sqrt{\log\log}\) blow-up in higher-order reaction-diffusion and wave equations: A formal “geometric” approach. Zbl 1178.35082
Galaktionov, V. A.
2
2009
Three types of self-similar blow-up for the fourth-order \(p\)-Laplacian equation with source. Zbl 1207.35196
Galaktionov, V. A.
1
2009
Third-order nonlinear dispersive equations: shocks, rarefaction, and blowup waves. Zbl 1177.76183
Galaktionov, V. A.; Pokhozhaev, S. I.
31
2008
Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation. Zbl 1152.35101
Galaktionov, V. A.; Mitidieri, E.; Pohozaev, S. I.
6
2008
Nonlinear dispersion equations: smooth deformations, compactions, and extensions to higher orders. Zbl 1177.76182
Galaktionov, V. A.
5
2008
Countable branching of similarity solutions of higher-order porous medium type equations. Zbl 1182.35070
Galaktionov, V. A.
5
2008
On blow-up space jets for the Navier-Stokes equations in \(\mathbb R^{3}\) with convergence to Euler equations. Zbl 1159.81322
Galaktionov, V. A.
4
2008
On nonexistence of Baras-Goldstein type without positivity assumptions for singular linear and nonlinear parabolic equations. Zbl 1233.35116
Galaktionov, V. A.
3
2008
Capacity induced by a nonlinear operator and applications. Zbl 1157.35305
Galaktionov, Victor A.; Mitidieri, Enzo; Pohozaev, Stanislav I.
3
2008
On higher-order viscosity approximations of odd-order nonlinear PDEs. Zbl 1173.76043
Galaktionov, Victor A.
3
2008
Hermitian spectral theory and blow-up patterns for a fourth-order semilinear Boussinesq equation. Zbl 1191.35230
Galaktionov, V. A.
2
2008
Non-radial very singular similarity solutions of absorption-diffusion equations with non-homogeneous potentials. Zbl 1152.35399
Galaktionov, V. A.
1
2008
\(L^{\infty }\) and decay estimates for higher-order semilinear diffusion-absorption equations. Zbl 1141.35010
Chaves, M.; Galaktionov, V. A.
1
2008
Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics. Zbl 1153.35001
Galaktionov, Victor A.; Svirshchevskii, Sergey R.
93
2007
Unstable sixth-order thin film equation. I: Blow-up similarity solutions. Zbl 1173.35562
Evans, J. D.; Galaktionov, V. A.; King, J. R.
23
2007
Source-type solutions of the fourth-order unstable thin film equation. Zbl 1156.35387
Evans, J. D.; Galaktionov, V. A.; King, J. R.
22
2007
Unstable sixth-order thin film equation. II: Global similarity patterns. Zbl 1173.35530
Evans, J. D.; Galaktionov, V. A.; King, J. R.
21
2007
Blow-up similarity solutions of the fourth-order unstable thin film equation. Zbl 1221.35296
Evans, J. D.; Galaktionov, V. A.; King, J. R.
16
2007
Sturmian nodal set analysis for higher-order parabolic equations and applications. Zbl 1160.35010
Galaktionov, V. A.
5
2007
Convergence in gradient systems with branching of equilibria. Zbl 1229.35078
Galaktionov, V. A.; Pohozaev, S. I.; Shishkov, A. E.
2
2007
Blowup for nonlinear initial-boundary value problems. Zbl 1327.35163
Galaktionov, V. A.; Pohozaev, S. I.
1
2007
Blow-up and global asymptotics of the limit unstable Cahn-Hilliard equation. Zbl 1110.35023
Evans, J. D.; Galaktionov, V. A.; Williams, J. F.
16
2006
Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators. Zbl 1109.35015
Galaktionov, V. A.; Pohozaev, S. I.
13
2006
Higher-order quasilinear parabolic equations with singular initial data. Zbl 1154.35374
Galaktionov, V. A.; Shishkov, A. E.
9
2006
On extensions of higher-order Hardy’s inequalities. Zbl 1212.35209
Galaktionov, Victor A.
5
2006
On interfaces and oscillatory solutions of higher-order semilinear parabolic equations with non-Lipschitz nonlinearities. Zbl 1145.35396
Galaktionov, V. A.
3
2006
Non-uniqueness and global similarity solutions for a higher-order semilinear parabolic equation. Zbl 1067.35032
Galaktionov, V. A.; Harwin, P. J.
11
2005
Self-similar boundary blow-up for higher-order quasilinear parabolic equations. Zbl 1099.35016
Galaktionov, V. A.; Shishkov, A. E.
5
2005
On evolution completeness of nonlinear eigenfunctions for the porous medium equation in the whole space. Zbl 1284.35217
Galaktionov, V. A.; Harwin, P. J.
3
2005
Sturm’s theorem on zero sets in nonlinear parabolic equations. Zbl 1094.35019
Galaktionov, Victor A.; Harwin, Petra J.
3
2005
Stabilization to a singular steady state for the Frank-Kamenetskii equation in a critical dimension. Zbl 1130.35077
Galaktionov, Victor A.; King, John R.
2
2005
On extensions of Hardy’s inequalities. Zbl 1330.26004
Galaktionov, Victor A.
2
2005
Geometric Sturmian theory of nonlinear parabolic equations and applications. Zbl 1075.35017
Galaktionov, Victor A.
43
2004
Global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1122.35040
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
29
2004
Self-similar blow-up in higher-order semilinear parabolic equations. Zbl 1112.35095
Budd, C. J.; Galaktionov, V. A.; Williams, J. F.
26
2004
On very singular similarity solutions of a higher-order semilinear parabolic equation. Zbl 1063.35077
Galaktionov, V. A.; Williams, J. F.
21
2004
A stability technique for evolution partial differential equations. A dynamical systems approach. Zbl 1065.35002
Galaktionov, Victor A.; Vázquez, Juan Luis
21
2004
Evolution completeness of separable solutions of nonlinear diffusion equations in bounded domains. Zbl 1065.35157
Galaktionov, V. A.
7
2004
Structure of boundary blow up for higher-order quasilinear parabolic equations. Zbl 1078.35043
Galaktionov, V. A.; Shishkov, A. E.
5
2004
On higher-order semilinear parabolic equations with measures as initial data. Zbl 1131.35346
Galaktionov, V. A.
1
2004
Blow-up and critical exponents for nonlinear hyperbolic equations. Zbl 1012.35058
Galaktionov, V. A.; Pohozaev, S. I.
32
2003
Saint-Venant’s principle in blow-up for higher-order quasilinear parabolic equations. Zbl 1064.35068
Galaktionov, V. A.; Shishkov, A. E.
15
2003
Intermediate asymptotics for inhomogeneous nonlinear heat conduction. Zbl 1205.35146
Galaktionov, V. A.; Kamin, S.; Kersner, R.; Vazquez, J. L.
12
2003
Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents. Zbl 1019.35042
Galaktionov, Victor A.; King, John R.
11
2003
On similarity solutions and blow-up spectra for a semilinear wave equation. Zbl 1039.35066
Galaktionov, V. A.; Pohozaev, S. I.
7
2003
Critical global asymptotics in higher-order semilinear parabolic equations. Zbl 1035.35048
Galaktionov, Victor A.
7
2003
Blow-up in a fourth-order semilinear parabolic equation from explosion-convection theory. Zbl 1052.35075
Galaktionov, V. A.; Williams, J. F.
5
2003
Lyapunov functionals in singular limits for perturbed quasilinear degenerate parabolic equations. Zbl 1058.35123
Chaves, Manuela; Galaktionov, Victor A.
1
2003
On uniqueness and stability of self-similar blow-up solutions of nonlinear heat equations: Evolution approach. Zbl 1050.35036
Chaves, Manuela; Galaktionov, Victor A.
1
2003
The problem of blow-up in nonlinear parabolic equations. Zbl 1010.35057
Galaktionov, Victor A.; Vázquez, Juan L.
134
2002
Existence and blow up for higher-order semilinear parabolic equations: majorizing order-preserving operators. Zbl 1082.35079
Galaktionov, V. A.; Pohozaev, S. I.
36
2002
On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range. Zbl 1020.35029
Egorov, Yu. V.; Galaktionov, V. A.; Kondratiev, V. A.; Pohozaev, S. I.
9
2002
Fast diffusion equation with critical Sobolev exponent in a ball. Zbl 0988.35088
Galaktionov, Victor A.; King, John R.
9
2002
Uniqueness of asymptotic profiles for an extinction problem. Zbl 1290.35141
Ferreira, R.; Galaktionov, V. A.; Vazquez, J. L.
6
2002
On uniqueness for ODEs arising in blow-up asymptotics for nonlinear heat equations. Zbl 1024.35050
Chaves, Manuela; Galaktionov, Victor A.
1
2002
On a spectrum of blow-up patterns for a higher-order semilinear parabolic equation. Zbl 0995.35009
Galaktionov, Victor A.
12
2001
Groups of scalings and invariant sets for higher-order nonlinear evolution equations. Zbl 1161.35425
Galaktionov, Victor A.
8
2001
Regional blow-up for a higher-order semilinear parabolic equation. Zbl 1002.35061
Chaves, Manuela; Galaktionov, Victor A.
8
2001
On the necessary conditions of global existence to a quasilinear inequality in the half-space. Zbl 0943.35110
Egorov, Yuri V.; Galaktionov, Victor A.; Kondratiev, Vladimir A.; Pohozaev, Stanislav I.
20
2000
Asymptotics of the fast-diffusion equation with critical exponent. Zbl 0954.35094
Galaktionov, Victor A.; Peletier, Lambertus A.; Vazquez, Juan L.
18
2000
Behaviour of interfaces in a diffusion-absorption equation with critical exponents. Zbl 0972.35101
Galaktionov, Victor A.; Shmarev, Sergei I.; Vazquez, Juan L.
4
2000
Quenching for a one-dimensional fully nonlinear parabolic equation in detonation theory. Zbl 0982.35008
Galaktionov, Victor A.; Gerbi, Stéphane; Vazquez, Juan L.
1
2000
Singularities for a 2-dimensional semilinear elliptic equation with a non-Lipschitz nonlinearity. Zbl 0927.35037
Bidaut-Véron, Marie-Françoise; Galaktionov, Victor; Grillot, Philippe; Véron, Laurent
13
1999
Regularity of interfaces in diffusion processes under the influence of strong absorption. Zbl 0938.35082
Galaktionov, Victor A.; Shmarev, S. I.; Vazquez, Juan L.
11
1999
Ordered invariant sets for KdV-type nonlinear evolution equations. Zbl 0972.35120
Galaktionov, V. A.
8
1999
...and 95 more Documents
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Cited by 1,345 Authors

71 Galaktionov, Victor Aleksandrovich
51 Mu, Chunlai
35 Vazquez, Juan Luis
28 Korpusov, Maksim Olegovich
21 Qu, Changzheng
19 Winkler, Michael
19 Zheng, Sining
18 Rossi, Julio Daniel
17 Fila, Marek
17 Souplet, Philippe
16 Xie, Chunhong
15 Semenov, Edward Ivanovich
15 Wang, Mingxin
15 Zhou, Jun
14 Álvarez-Caudevilla, Pablo
14 Iagar, Razvan Gabriel
14 King, John Robert
14 Liu, Chein-Shan
14 Yin, Jingxue
12 Ding, Juntang
12 Pokhozhaev, Stanislav I.
11 Liu, Bingchen
11 Mizoguchi, Noriko
10 de Pablo, Arturo
10 Ferreira, Raúl
10 Kaikina, Elena Igorevna
10 Kosov, Aleksandr Arkad’evich
10 Qi, Yuanwei
10 Sánchez, Ariel
10 Xiang, Zhaoyin
10 Zhang, Zhengce
10 Zheng, Pan
9 Guo, Jong-Shenq
9 Han, Yuzhu
9 Li, Zhongping
9 Quirós Gracián, Fernando
9 Shishkov, Andrey E.
9 Yanagida, Eiji
9 Yang, Zuodong
8 Broadbridge, Philip
8 Deng, Weibing
8 Ishige, Kazuhiro
8 Kirane, Mokhtar
8 Levine, Howard Allen
8 Li, Yuxiang
8 Polyanin, Andrei D.
8 Tersenov, Alkis Savvich
7 Budd, Christopher John
7 Diaz Diaz, Jesus Ildefonso
7 Du, Lili
7 Fang, Zhongbo
7 Fiedler, Bernold
7 Groisman, Pablo
7 Hayashi, Nakao
7 Herrero, Miguel Ángel
7 Ji, Lina
7 Laurençot, Philippe
7 Mitidieri, Enzo Luigi
7 Naumkin, Pavel Ivanovich
7 Panin, Aleksandr Anatol’evich
7 Pao, Chia-Ven
7 Quittner, Pavol
6 Antontsev, Stanislav Nikolaevich
6 Chaves, Manuela
6 Cherniha, Roman M.
6 Evans, Jonathan David
6 Gao, Wenjie
6 Hsu, Shu-Yu
6 Hu, Bei
6 Kazakov, Aleksandr Leonidovich
6 Liang, Zhilei
6 Pérez-Llanos, Mayte
6 Popovych, Roman O.
6 Rocha, Carlos
6 Rodríguez-Bernal, Aníbal
6 Velázquez, Juan J. L.
6 Wang, Zejia
6 Yang, Chunxiao
6 Zaag, Hatem
5 Bradshaw-Hajek, Bronwyn H.
5 Chen, Shaohua
5 Cortázar, Carmen
5 Elgueta, Manuel
5 Guo, Bao-Zhu
5 Jin, Chunhua
5 Kawakami, Tatsuki
5 Kon’kov, Andrej A.
5 Kurkina, Elena S.
5 Lacey, Andrew A.
5 Li, Fengjie
5 Liu, Dengming
5 Matano, Hiroshi
5 Mi, Yongsheng
5 Naito, Yūki
5 Rudykh, Gennady Alekseevich
5 Shmarev, Sergei I.
5 Véron, Laurent
5 Zheng, Gao-Feng
4 Ahmad, Bashir
4 Al-saedi, Ahmed Eid Salem
...and 1,245 more Authors
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Cited in 234 Serials

124 Journal of Mathematical Analysis and Applications
112 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
86 Journal of Differential Equations
31 Applied Mathematics Letters
27 Applicable Analysis
24 Applied Mathematics and Computation
24 Journal of Computational and Applied Mathematics
22 Communications in Partial Differential Equations
21 Computers & Mathematics with Applications
21 Differential Equations
21 Nonlinear Analysis. Theory, Methods & Applications
20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
19 ZAMP. Zeitschrift für angewandte Mathematik und Physik
17 Mathematical Methods in the Applied Sciences
17 Boundary Value Problems
16 Journal of Functional Analysis
16 Communications in Nonlinear Science and Numerical Simulation
15 Mathematische Annalen
15 Journal of Mathematical Sciences (New York)
15 Discrete and Continuous Dynamical Systems
15 Nonlinear Analysis. Real World Applications
14 Journal of Mathematical Physics
14 Calculus of Variations and Partial Differential Equations
14 Abstract and Applied Analysis
13 Proceedings of the American Mathematical Society
13 Physica D
12 Mathematical Notes
12 Theoretical and Mathematical Physics
11 Siberian Mathematical Journal
10 Studies in Applied Mathematics
10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
9 Mathematical and Computer Modelling
9 Journal de Mathématiques Pures et Appliquées. Neuvième Série
9 Advances in Nonlinear Analysis
8 Journal of Computational Physics
8 Rocky Mountain Journal of Mathematics
8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
8 Transactions of the American Mathematical Society
8 Computational Mathematics and Mathematical Physics
8 Journal of Dynamics and Differential Equations
8 NoDEA. Nonlinear Differential Equations and Applications
8 Communications in Contemporary Mathematics
8 Journal of Evolution Equations
8 Advanced Nonlinear Studies
7 Advances in Mathematics
7 Acta Mathematica Sinica. English Series
7 Communications on Pure and Applied Analysis
7 Proceedings of the Steklov Institute of Mathematics
6 Journal of Engineering Mathematics
6 Ukrainian Mathematical Journal
6 Archiv der Mathematik
6 Acta Applicandae Mathematicae
6 Computational Mathematics and Modeling
6 Doklady Mathematics
6 Comptes Rendus. Mathématique. Académie des Sciences, Paris
6 Science China. Mathematics
6 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika
5 Archive for Rational Mechanics and Analysis
5 Reports on Mathematical Physics
5 European Journal of Applied Mathematics
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4 Israel Journal of Mathematics
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4 Chaos, Solitons and Fractals
4 Glasgow Mathematical Journal
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4 Journal of Inequalities and Applications
4 The ANZIAM Journal
4 Discrete and Continuous Dynamical Systems. Series B
4 Mediterranean Journal of Mathematics
4 Discrete and Continuous Dynamical Systems. Series S
3 Journal d’Analyse Mathématique
3 Prikladnaya Matematika i Mekhanika
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Mathematische Zeitschrift
3 Publications of the Research Institute for Mathematical Sciences, Kyoto University
3 Zeitschrift für Analysis und ihre Anwendungen
3 Science in China. Series A
3 The Journal of Geometric Analysis
3 SIAM Journal on Mathematical Analysis
3 Electronic Journal of Differential Equations (EJDE)
3 Chaos
3 Fractional Calculus & Applied Analysis
3 Journal of Dynamical and Control Systems
3 Dynamical Systems
3 Central European Journal of Mathematics
3 Analysis and Applications (Singapore)
3 Complex Variables and Elliptic Equations
3 Journal of Nonlinear Science and Applications
3 International Journal of Differential Equations
2 Communications on Pure and Applied Mathematics
2 Journal of Applied Mathematics and Mechanics
2 Computing
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Cited in 45 Fields

1,234 Partial differential equations (35-XX)
109 Fluid mechanics (76-XX)
75 Numerical analysis (65-XX)
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37 Dynamical systems and ergodic theory (37-XX)
36 Global analysis, analysis on manifolds (58-XX)
28 Classical thermodynamics, heat transfer (80-XX)
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15 Statistical mechanics, structure of matter (82-XX)
13 Systems theory; control (93-XX)
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8 Functional analysis (46-XX)
8 Calculus of variations and optimal control; optimization (49-XX)
6 Topological groups, Lie groups (22-XX)
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4 History and biography (01-XX)
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