## Payne, Lawrence Edward

Compute Distance To:
 Author ID: payne.lawrence-edward Published as: Payne, L. E.; Payne, Lawrence E.; Payne, Laurent E.; Payne, Lawrence Edward more...less External Links: MGP · Wikidata
 Documents Indexed: 291 Publications since 1949, including 2 Books 1 Contribution as Editor · 2 Further Contributions Reviewing Activity: 2 Reviews Biographic References: 2 Publications Co-Authors: 40 Co-Authors with 241 Joint Publications 1,023 Co-Co-Authors
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### Co-Authors

 52 single-authored 35 Philippin, Gérard A. 28 Song, Jong Chul 26 Knops, Robin J. 25 Schaefer, Philip W. 25 Straughan, Brian 20 Bramble, James H. 19 Ames, Karen A. 18 Horgan, Cornelius Oliver 12 Weinberger, Hans Felix 11 Lin, Changhao 8 Levine, Howard Allen 5 Sather, Duane 4 Diaz, Joaquin Basilio 4 Flavin, James N. 4 Hersch, Joseph 4 Vernier-Piro, Stella 3 Pell, William H. 3 Pólya, George 3 Sperb, Rene P. 3 Stakgold, Ivar 2 Dassios, George 2 Morro, Angelo 2 Rayner, Margaret Eva 2 Webb, Jeffrey Ronald Leslie 2 Weinstein, Alexander 2 Wheeler, Lewis T. 1 Acker, Andrew F. 1 Anger, Gottfried 1 Bamberger, Alain 1 Beckenbach, Edwin Ford 1 Björck, Åke 1 Bohlin, Torsten 1 Chavent, Guy 1 Cifka, J. 1 Crooke, Philip S. III 1 de Bruijn, Nicolaas Govert 1 Deregowski, S. M. 1 Edholm, Paul 1 Eldén, Lars 1 Elfving, Tommy 1 Engquist, Bjorn E. 1 Fan, Ky 1 Friedman, Avner 1 Galdi, Giovanni Paolo 1 Glashoff, Klaus 1 Gosselin, Richard P. 1 Granlund, Gösta H. 1 Gustafson, Sven-Åke 1 Gustafsson, Bertil 1 Hosken, J. W. J. 1 Ingemarsson, Ingemar 1 Karlin, Samuel 1 Khosrovshahi, Gholamreza B. 1 Knutsson, Hans 1 Kristensson, Gerhard 1 Lailly, Patrick 1 Littlewood, John Edensor 1 Ljung, Lennart 1 Marcus, Marvin D. 1 Marek, Ivo 1 Marshall, Albert W. 1 Metcalf, Frederic T. 1 Moler, Cleve B. 1 Motzkin, Theodore Samuel 1 Nashed, M. Zuhair 1 Natterer, Frank 1 Niordson, Frithiof I. N. 1 Nordling, Nikus 1 Olhoff, Niels 1 Olkin, Ingram 1 Philip, Johan 1 Pironneau, Olivier 1 Pokorná, Olga 1 Proctor, Michael Richard Edward 1 Proschan, Frank 1 Rasmussen, Steen Hojlund 1 Rionero, Salvatore 1 Rodrigues, José Francisco 1 Sacks, Paul E. 1 Safoui, Abdessalam 1 Sattinger, David H. 1 Schiffer, Menahem Max 1 Schoenberg, Isaac Jacob 1 Shisha, D. 1 Shisha, Oved 1 Simmonds, James G. 1 Ström, Staffan 1 Sundström, Arne 1 Taussky-Todd, Olga 1 Todd, John 1 Wahba, Grace 1 Wedin, Per-Åke 1 Weiss, George-Herbert 1 Wold, Svante 1 Ziegler, Zvi
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### Serials

 24 Journal of Mathematical Analysis and Applications 19 Archive for Rational Mechanics and Analysis 19 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 SIAM Journal on Mathematical Analysis 11 Applicable Analysis 11 Quarterly of Applied Mathematics 11 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 10 Journal of Elasticity 10 Nonlinear Analysis. Theory, Methods & Applications 9 Mathematical Methods in the Applied Sciences 8 International Journal of Engineering Science 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Journal of Research of the National Bureau of Standards 7 Journal of Mathematics and Physics 4 Duke Mathematical Journal 4 Pacific Journal of Mathematics 4 Studies in Applied Mathematics 3 IMA Journal of Applied Mathematics 3 Journal d’Analyse Mathématique 3 Quarterly Journal of Mechanics and Applied Mathematics 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 SIAM Journal on Applied Mathematics 3 Journal of the Society for Industrial & Applied Mathematics 2 Geophysical and Astrophysical Fluid Dynamics 2 International Journal of Non-Linear Mechanics 2 International Journal of Solids and Structures 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Differential Equations 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Differential and Integral Equations 2 Mathematics and Mechanics of Solids 2 Mathematical Inequalities & Applications 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Proceedings of the Cambridge Philosophical Society 2 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 American Mathematical Monthly 1 Communications on Pure and Applied Mathematics 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Israel Journal of Mathematics 1 Journal of Fluid Mechanics 1 Rocky Mountain Journal of Mathematics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica 1 Mathematika 1 Meccanica 1 Portugaliae Mathematica 1 SIAM Journal on Numerical Analysis 1 Advances in Applied Mathematics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Zeitschrift für Analysis und ihre Anwendungen 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Journal of Non-Equilibrium Thermodynamics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 Continuum Mechanics and Thermodynamics 1 Journal of Inequalities and Applications 1 International Journal of Pure and Applied Mathematics 1 Journal of Applied Physics 1 Rendiconti di Matematica, VI. Serie 1 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Journal of Rational Mechanics and Analysis
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### Fields

 187 Partial differential equations (35-XX) 54 Mechanics of deformable solids (74-XX) 38 Fluid mechanics (76-XX) 11 Classical thermodynamics, heat transfer (80-XX) 8 Potential theory (31-XX) 6 Ordinary differential equations (34-XX) 4 Operator theory (47-XX) 3 General and overarching topics; collections (00-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Biology and other natural sciences (92-XX) 2 Real functions (26-XX) 2 Differential geometry (53-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

261 Publications have been cited 4,637 times in 2,765 Documents Cited by Year
Saddle points and instability of nonlinear hyperbolic equations. Zbl 0317.35059
Payne, L. E.; Sattinger, D. H.
1976
An optimal Poincaré inequality for convex domains. Zbl 0099.08402
Payne, L. E.; Weinberger, H. F.
1960
Improperly posed problems in partial differential equations. Zbl 0302.35003
Payne, L. E.
1975
Isoperimetric inequalities and their applications. Zbl 0154.12602
Payne, L. E.
1967
On the ratio of consecutive eigenvalues. Zbl 0073.08203
Payne, Laurent E.; Pólya, George; Weinberger, Hans F.
1956
Uniqueness theorems in linear elasticity. Zbl 0224.73016
Knops, R. J.; Payne, L. E.
1971
Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Zbl 1110.35031
Payne, L. E.; Schaefer, P. W.
2007
Lower bounds for blow-up time in parabolic problems under Neumann conditions. Zbl 1110.35032
Payne, L. E.; Schaefer, P. W.
2006
Convergence and continuous dependence for the Brinkman-Forchheimer equations. Zbl 1136.76448
Payne, L. E.; Straughan, B.
1999
Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. Zbl 0906.35067
Payne, L. E.; Straughan, B.
1998
Decay estimates for the constrained elastic cylinder of variable cross section. Zbl 0706.73015
Flavin, J. N.; Knops, R. J.; Payne, L. E.
1989
New bounds for solutions of second order elliptic partial differential equations. Zbl 0093.10901
Payne, L. E.; Weinberger, H. F.
1958
Blow-up phenomena for some nonlinear parabolic problems. Zbl 1159.35382
Payne, L. E.; Philippin, G. A.; Schaefer, P. W.
2008
On inequalities of Korn, Friedrichs and Babuska-Aziz. Zbl 0512.73017
Horgan, C. O.; Payne, L. E.
1983
The Stokes flow problem for a class of axially symmetric bodies. Zbl 0091.42202
Payne, L. E.; Pell, W. H.
1960
Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Zbl 0933.76091
Payne, L. E.; Song, J. C.; Straughan, B.
1999
Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II. Zbl 1198.35131
Payne, L. E.; Philippin, G. A.; Piro, S. Vernier
2010
Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Zbl 1184.35077
Payne, L. E.; Schaefer, P. W.
2009
Spatial decay estimates in transient heat conduction. Zbl 0553.35037
Horgan, C. O.; Payne, L. E.; Wheeler, L. T.
1984
Bounds for blow-up time in nonlinear parabolic problems. Zbl 1139.35055
Payne, L. E.; Philippin, G. A.; Schaefer, P. W.
2008
Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. I. Zbl 1227.35173
Payne, L. E.; Philippin, G. A.; Vernier Piro, S.
2010
Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elasto- dynamics. Zbl 0292.35067
Knops, R. J.; Levine, H. A.; Payne, L. E.
1974
Some isoperimetric inequalities for membrane frequencies and torsional rigidity. Zbl 0098.39201
Payne, L. E.; Weinberger, H. F.
1961
Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature. Zbl 0408.35015
Payne, L. E.; Philippin, G. A.
1979
Lower bounds for blow-up time in a nonlinear parabolic problem. Zbl 1177.35043
Payne, L. E.; Song, J. C.
2009
Some isoperimetric inequalities for harmonic functions. Zbl 0199.16902
Payne, L. E.
1970
On the mean value of the fundamental mode in the fixed membrane problem. Zbl 0323.35057
Payne, L. E.; Stakgold, I.
1973
Duality theorems in some overdetermined boundary value problems. Zbl 0698.35051
Payne, L. E.; Schaefer, Philip W.
1989
Bounds in the Cauchy problem for the Laplace equation. Zbl 0094.29801
Payne, L. E.
1960
Energy bounds in dynamical problems for a semi-infinite elastic beam. Zbl 0736.73035
Flavin, J. N.; Knops, R. J.; Payne, L. E.
1990
On two conjectures in the fixed membrane eigenvalue problem. Zbl 0272.35058
Payne, Lawrence E.
1973
Some inequalities for Stekloff eigenvalues. Zbl 0315.35069
Hersch, J.; Payne, L. E.; Schiffer, M. M.
1974
Structural stability for the Darcy equations of flow in porous media. Zbl 0912.76088
Payne, L. E.; Straughan, B.
1998
Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics. Zbl 0227.35017
Knops, R. J.; Payne, L. E.
1971
On Korn’s inequality. Zbl 0107.31105
Payne, L. E.; Weinberger, H. F.
1961
Inequalities for eigenvalues of membranes and plates. Zbl 0064.34802
Payne, L. E.
1955
Sur le quotient de deux fréquences propres consécutives. Zbl 0065.08801
Payne, Laurent E.; Pólya, George; Weinberger, Hans F.
1955
Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media. Zbl 0848.76089
Payne, L. E.; Straughan, B.
1996
Effect of anisotropic permeability on Darcy’s law. Zbl 0984.76024
Payne, L. E.; Rodrigues, J. F.; Straughan, B.
2001
Some applications of the maximum principle in the problem of torsional creep. Zbl 0378.73028
Payne, L. E.; Philippin, G. A.
1977
Lower bounds for vibration frequencies of elastically supportes membranes and plates. Zbl 0083.19406
Payne, L. E.; Weinberger, H. F.
1957
Continuous data dependence for the equations of classical elastodynamics. Zbl 0184.51004
Knops, R. J.; Payne, L. E.
1969
Lower bounds for blow-up in a model of chemotaxis. Zbl 1231.35027
Payne, L. E.; Song, J. C.
2012
Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Zbl 0982.35119
Ames, K. A.; Payne, L. E.
1998
Some remarks on maximum principles. Zbl 0334.35029
Payne, L. E.
1976
On the stability of solutions of Navier-Stokes equations backward in time. Zbl 0159.14201
Knops, R. J.; Payne, L. E.
1968
Structural stability for a Brinkman fluid. Zbl 1208.35011
Lin, Changhao; Payne, L. E.
2007
Decay estimates in steady pipe flow. Zbl 0675.76029
Ames, K. A.; Payne, L. E.
1989
An isoperimetric inequality for the first eigenfunction in the fixed membrane problem. Zbl 0241.73080
Payne, Lawrence E.; Rayner, Margaret E.
1972
New bounds in harmonic and biharmonic problems. Zbl 0064.09903
Payne, L. E.; Weinberger, H. F.
1955
On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity. Zbl 0209.56605
Knops, R. J.; Payne, L. E.
1970
Nonlinear problems in nuclear reactor analysis. Zbl 0259.35025
Stakgold, I.; Payne, L. E.
1973
Analysis of convective reaction-diffusion equation. II. Zbl 0702.35126
Levine, H. A.; Payne, L. E.; Sacks, P. E.; Straughan, B.
1989
Decay, growth, continuous dependence and uniqueness results in generalized heat conduction theories. Zbl 0694.35007
Morro, A.; Payne, L. E.; Straughan, B.
1990
Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Zbl 1277.35075
Payne, L. E.; Philippin, G. A.
2013
New isoperimetric inequalities for eigenvalues and other physical quantities. Zbl 0074.31405
Payne, L. E.
1956
Blow-up in parabolic problems under Robin boundary conditions. Zbl 1156.35408
Payne, L. E.; Schaefer, P. W.
2008
On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem. Zbl 0508.73051
Acker, A.; Payne, L. E.; Philippin, G.
1981
Energy and pointwise bounds in some non-standard parabolic problems. Zbl 1056.35104
Ames, K. A.; Payne, L. E.; Schaefer, P. W.
2004
Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Zbl 0893.76090
Payne, L. E.; Song, J. C.
1997
Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. Zbl 1139.35085
Lin, Changhao; Payne, L. E.
2008
On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Zbl 0819.76077
Ames, K. A.; Payne, L. E.
1994
Bounds for eigenvalues and eigenvectors of symmetric operators. Zbl 0159.44204
Moler, C. B.; Payne, L. E.
1968
Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid. Zbl 0681.76013
Payne, L. E.; Straughan, B.
1989
Decay estimates for second-order quasilinear partial differential equations. Zbl 0556.35053
Horgan, C. O.; Payne, L. E.
1984
Structural stability for the Brinkman equations of flow in double diffusive convection. Zbl 1167.35435
Lin, Changhao; Payne, L. E.
2007
Uniqueness in classical elastodynamics. Zbl 0159.56201
Knops, R. J.; Payne, L. E.
1967
Extreme principles and isoperimetric inequalities for some mixed problems of Stekloff’s type. Zbl 0165.12603
Hersch, J.; Payne, L. E.
1968
Convection in thawing subsea permafrost. Zbl 0645.76055
Galdi, G. P.; Payne, L. E.; Proctor, M. R. E.; Straughan, B.
1987
Improved estimates for continuous data dependence in linear elastodynamics. Zbl 0663.73009
Knops, R. J.; Payne, L. E.
1988
Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints. Zbl 0293.35004
Levine, H. A.; Payne, L. E.
1974
Stability in linear elasticity. Zbl 0182.58905
Knops, R. J.; Payne, L. E.
1968
Spatial decay estimates in time-dependent Stokes flow. Zbl 0787.35060
Ames, K. A.; Payne, L. E.; Schaefer, P. W.
1993
Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Zbl 1136.35318
Payne, L. E.; Straughan, B.
2000
Decay estimates for a class of nonlinear boundary value problems in two dimensions. Zbl 0678.35027
Horgan, C. O.; Payne, L. E.
1989
Some non-standard problems in viscous flow. Zbl 1174.76307
Payne, L. E.; Schaefer, P. W.; Song, J. C.
2004
Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions. Zbl 0790.31002
Horgan, C. O.; Payne, L. E.
1993
Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows. Zbl 0970.76097
Payne, L. E.; Song, J. C.
2000
Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Zbl 0928.35015
Ames, K. A.; Payne, L. E.
1999
Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions. Zbl 1255.35059
Payne, L. E.; Philippin, G. A.
2012
On some maximum principles involving harmonic functions and their derivatives. Zbl 0402.35014
Payne, L. E.; Philippin, G. A.
1979
A Saint-Venant principle for nonlinear elasticity. Zbl 0519.73005
Knops, R. J.; Payne, L. E.
1983
On a priori bounds in the Cauchy problem for elliptic equations. Zbl 0199.16603
Payne, L. E.
1970
Some inequalities for vector functions with applications in elasticity. Zbl 0109.16806
Bramble, J. H.; Payne, L. E.
1962
Bounds in the Neumann problem for second order uniformly elliptic operators. Zbl 0111.09701
Bramble, J. H.; Payne, L. E.
1962
Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Zbl 1241.35027
Payne, L. E.; Philippin, G. A.
2012
Note on a lemma of Finn and Gilbar. Zbl 0078.40002
Payne, L. E.; Weinberger, H. F.
1957
Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder. Zbl 0762.35012
Flavin, J. N.; Knops, R. J.; Payne, L. E.
1992
Some Phragmén-Lindelöf type results for the biharmonic equation. Zbl 0810.31001
Payne, L. E.; Schaefer, P. W.
1994
Energy bounds for some nonstandard problems in partial differential equations. Zbl 1121.35331
Payne, L. E.; Schaefer, P. W.
2002
On two free boundary problems in potential theory. Zbl 0760.31003
Payne, L. E.; Philippin, G. A.
1991
Isoperimetric inequalities in the torsion and clamped membrane problems for convex plane domains. Zbl 0521.73056
Payne, L. E.; Philippin, G. A.
1983
Decay bounds for solutions of second order parabolic problems and their derivatives. Zbl 0832.35019
Payne, L. E.; Philippin, G. A.
1995
Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function. Zbl 0481.35022
Payne, L. E.
1981
Some isoperimetric norm bounds for solutions of the Helmholtz equation. Zbl 0256.35023
Payne, Lawrence E.; Rayner, Margaret E.
1973
Some general remarks on improperly posed problems for partial differential equations. Zbl 0257.35079
Payne, L. E.
1973
Uniqueness and continuous dependence criteriafor the Navier-Stokes equations. Zbl 0259.35068
Payne, L. E.
1972
Spatial decay bounds in the channel flow of an incompressible viscous fluid. Zbl 1185.35024
Lin, Changhao; Payne, Lawrence E.
2004
A Faber-Krahn inequality for wedge-like membranes. Zbl 0099.18701
Payne, L. E.; Weinberger, H. F.
1960
On Stokes flow about a torus. Zbl 0099.20204
Pell, W. H.; Payne, L. E.
1960
Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Zbl 1277.35075
Payne, L. E.; Philippin, G. A.
2013
Lower bounds for blow-up in a model of chemotaxis. Zbl 1231.35027
Payne, L. E.; Song, J. C.
2012
Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions. Zbl 1255.35059
Payne, L. E.; Philippin, G. A.
2012
Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Zbl 1241.35027
Payne, L. E.; Philippin, G. A.
2012
Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II. Zbl 1198.35131
Payne, L. E.; Philippin, G. A.; Piro, S. Vernier
2010
Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. I. Zbl 1227.35173
Payne, L. E.; Philippin, G. A.; Vernier Piro, S.
2010
Blow-up and decay criteria for a model of chemotaxis. Zbl 1195.35058
Payne, L. E.; Song, J. C.
2010
Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Zbl 1184.35077
Payne, L. E.; Schaefer, P. W.
2009
Lower bounds for blow-up time in a nonlinear parabolic problem. Zbl 1177.35043
Payne, L. E.; Song, J. C.
2009
Decay for a Keller-Segel chemotaxis model. Zbl 1180.35529
Payne, L. E.; Straughan, B.
2009
An ill-posed problem for the heat equation. Zbl 1179.35339
Payne, L. E.; Philippin, G. A.
2009
Blow-up phenomena for some nonlinear parabolic problems. Zbl 1159.35382
Payne, L. E.; Philippin, G. A.; Schaefer, P. W.
2008
Bounds for blow-up time in nonlinear parabolic problems. Zbl 1139.35055
Payne, L. E.; Philippin, G. A.; Schaefer, P. W.
2008
Blow-up in parabolic problems under Robin boundary conditions. Zbl 1156.35408
Payne, L. E.; Schaefer, P. W.
2008
Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. Zbl 1139.35085
Lin, Changhao; Payne, L. E.
2008
Blow-up phenomena for some nonlinear parabolic systems. Zbl 1169.35340
Payne, L. E.; Schaefer, P. W.
2008
Spatial decay bounds for double diffusive convection in Brinkman flow. Zbl 1133.35021
Payne, L. E.; Song, J. C.
2008
Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Zbl 1110.35031
Payne, L. E.; Schaefer, P. W.
2007
Structural stability for a Brinkman fluid. Zbl 1208.35011
Lin, Changhao; Payne, L. E.
2007
Structural stability for the Brinkman equations of flow in double diffusive convection. Zbl 1167.35435
Lin, Changhao; Payne, L. E.
2007
Lower bounds for the blow-up time in a temperature dependent Navier-Stokes flow. Zbl 1124.35057
Payne, L. E.; Song, J. C.
2007
A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov. Zbl 1136.35110
Payne, L. E.
2007
Spatial decay in a double diffusive convection problem in Darcy flow. Zbl 1110.76051
Payne, L. E.; Song, J. C.
2007
Continuous dependence on the geometry and on the initial time for a class of parabolic problems. I. Zbl 1133.35010
Payne, L. E.; Philippin, G. A.; Proytcheva, V.
2007
Spatial decay in a cross-diffusion problem. Zbl 1134.35018
Payne, L. E.; Song, J. C.
2007
Lower bounds for blow-up time in parabolic problems under Neumann conditions. Zbl 1110.35032
Payne, L. E.; Schaefer, P. W.
2006
On a proposed model for heat conduction. Zbl 1126.80003
Payne, L. E.; Song, J. C.
2006
Decay bounds for solutions of second order parabolic problems and their derivatives. IV. Zbl 1096.35065
Payne, L. E.; Philippin, G. A.; Piro, S. Vernier
2006
Blow up, decay bounds and continuous dependence inequalities for a class of quasilinear parabolic problems. Zbl 1138.35037
Payne, L. E.; Philippin, G. A.; Vernier-Piro, S.
2006
Continuous dependence inequalities for a class of quasilinear parabolic problems. Zbl 1100.35013
Payne, L. E.; Philippin, G. A.; Safoui, A.
2006
Some nonstandard problems in generalized heat conduction. Zbl 1080.35034
Payne, L. E.; Schaefer, P. W.; Song, J. C.
2005
Alternative spatial growth and decay for constrained motion in an elastic cylinder. Zbl 1074.74009
Knops, R. J.; Payne, L. E.
2005
Improved spatial decay bounds in generalized heat conduction. Zbl 1082.35078
Payne, L. E.; Song, J. C.
2005
Spatial decay bounds for a class of quasi-linear parabolic initial-boundary value problems. Zbl 1349.35173
Payne, L. E.; Philippin, G. A.
2005
On two classes of nonstandard parabolic problems. Zbl 1083.35132
Ames, K. A.; Payne, L. E.; Song, J. C.
2005
Energy and pointwise bounds in some non-standard parabolic problems. Zbl 1056.35104
Ames, K. A.; Payne, L. E.; Schaefer, P. W.
2004
Some non-standard problems in viscous flow. Zbl 1174.76307
Payne, L. E.; Schaefer, P. W.; Song, J. C.
2004
Spatial decay bounds in the channel flow of an incompressible viscous fluid. Zbl 1185.35024
Lin, Changhao; Payne, Lawrence E.
2004
On a nonstandard problem for heat conduction in a cylinder. Zbl 1052.35066
Ames, K. A.; Payne, L. E.; Schaefer, P. W.
2004
Spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid. Zbl 1075.35054
Lin, Changhao; Payne, Lawrence E.
2004
Decay bounds for solutions of second order parabolic problems and their derivatives. III. Zbl 1072.35097
Payne, L. E.; Philippin, G. A.
2004
Decay bounds for solutions of second order parabolic problems and their derivatives. II. Zbl 1069.35506
Payne, L. E.; Philippin, G. A.
2004
Continuous dependence of heat flux on spatial geometry for the generalized Maxwell-Cattaneo system. Zbl 1054.35007
Lin, Changhao; Payne, L. E.
2004
Improved bounds for some nonstandard problems in generalized heat conduction. Zbl 1065.35081
Payne, L. E.; Schaefer, P. W.; Song, J. C.
2004
Spatial decay estimates for the Maxwell-Cattaneo equations with mixed boundary conditions. Zbl 1065.35134
Payne, L. E.; Song, J. C.
2004
Temporal decay bounds in generalized heat conduction. Zbl 1058.35142
Payne, L. E.; Song, J. C.
2004
Energy bounds for some nonstandard problems in partial differential equations. Zbl 1121.35331
Payne, L. E.; Schaefer, P. W.
2002
Spatial decay bounds for the Forchheimer equations. Zbl 1211.76119
Payne, L. E.; Song, J. C.
2002
Decay bounds in initial-boundary value problems for nonlinear parabolic systems. Zbl 1011.35072
Payne, L. E.; Schaefer, P. W.
2002
Growth and decay in generalized thermoelasticity. Zbl 1211.74076
Payne, L. E.; Song, J. C.
2002
Effect of anisotropic permeability on Darcy’s law. Zbl 0984.76024
Payne, L. E.; Rodrigues, J. F.; Straughan, B.
2001
Spatial decay in the pipe flow of a viscous fluid interfacing a porous medium. Zbl 1034.35103
Ames, K. A.; Payne, L. E.; Song, J. C.
2001
Continuous dependence on spatial geometry for the generalized Maxwell-Cattaneo system. Zbl 0994.35024
Lin, Changhao; Payne, L. E.
2001
Eigenvalue and eigenfunction inequalities for the elastically supported membrane. Zbl 0986.35081
Payne, L. E.; Schaefer, P. W.
2001
Convergence results for generalized heat condution as the relaxation time tends to zero. Zbl 0977.35015
Payne, L. E.; Song, J. C.
2001
Continuous dependence on base data in an elastic prismatic cylinder. Zbl 1034.74007
Knops, R. J.; Payne, L. E.
2001
Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Zbl 1136.35318
Payne, L. E.; Straughan, B.
2000
Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows. Zbl 0970.76097
Payne, L. E.; Song, J. C.
2000
A naturally efficient numerical technique for porous convection stability with non-trivial boundary conditions. Zbl 0977.76070
Payne, L. E.; Straughan, B.
2000
On the spatial decay of solutions to a quasi-linear parabolic initial-boundary value problem and their derivatives. Zbl 0963.35091
Payne, L. E.; Philippin, G. A.
2000
Convergence and continuous dependence for the Brinkman-Forchheimer equations. Zbl 1136.76448
Payne, L. E.; Straughan, B.
1999
Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Zbl 0933.76091
Payne, L. E.; Song, J. C.; Straughan, B.
1999
Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Zbl 0928.35015
Ames, K. A.; Payne, L. E.
1999
Convergence of the equations for a Maxwell fluid. Zbl 1136.76310
Payne, L. E.; Straughan, B.
1999
Growth and decay results in heat conduction problems with nonlinear boundary conditions. Zbl 0919.35066
Payne, L. E.; Schaefer, P. W.; Song, J. C.
1999
Effect of errors in the spatial geometry for temperature dependent Stokes flow. Zbl 0935.76020
Payne, L. E.; Straughan, B.
1999
Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. Zbl 0906.35067
Payne, L. E.; Straughan, B.
1998
Structural stability for the Darcy equations of flow in porous media. Zbl 0912.76088
Payne, L. E.; Straughan, B.
1998
Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Zbl 0982.35119
Ames, K. A.; Payne, L. E.
1998
Bounds and decay results for some second-order semilinear elliptic problems. Zbl 0917.35036
Payne, L. E.; Schaefer, P. W.; Song, J. C.
1998
Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Zbl 0893.76090
Payne, L. E.; Song, J. C.
1997
Continuous dependence on the initial-time geometry in generalized heat conduction. Zbl 0871.35013
Payne, L. E.; Song, J. C.
1997
Continuous dependence results for a problem in penetrative convection. Zbl 0892.35079
Ames, Karen A.; Payne, Lawrence E.
1997
Saint-Venant’s principle in linear isotropic elasticity for incompressible or nearly incompressible materials. Zbl 0907.73010
Horgan, C. O.; Payne, L. E.
1997
Continuous dependence on initial-time and spatial geometry in generalized heat conduction. Zbl 0889.35011
Payne, L. E.; Song, J. C.
1997
Continuous dependence results for an ill-posed problem in nonlinear viscoelasticity. Zbl 0906.73030
Ames, Karen A.; Payne, Lawrence E.
1997
Spatial decay estimates for a coupled system of second-order quasilinear partial differential equations arising in thermoelastic finite anti-plane shear. Zbl 0887.35051
Horgan, C. O.; Payne, L. E.
1997
Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media. Zbl 0848.76089
Payne, L. E.; Straughan, B.
1996
Phragmén-Lindelöf and continuous dependence type results in generalized heat conduction. Zbl 0864.35051
Payne, L. E.; Song, J. C.
1996
The effect of a variation in the elastic moduli on Saint-Venant’s principle for a half-cylinder. Zbl 0890.73014
Knops, R. J.; Payne, L. E.
1996
Spatial decay estimates for a class of second-order quasilinear elliptic partial differential equations arising in anisotropic nonlinear elasticity. Zbl 1001.74524
Horgan, C. O.; Payne, L. E.
1996
A special class of maximum principles with applications to nonlinear boundary value problems. Zbl 0845.35013
Payne, L. E.
1996
Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region. Zbl 0884.35041
Knops, R. J.; Payne, L. E.
1996
Decay bounds for solutions of second order parabolic problems and their derivatives. Zbl 0832.35019
Payne, L. E.; Philippin, G. A.
1995
Continuous dependence on initial-time geometry for a thermoelastic system with sign-indefinite elasticities. Zbl 0857.35128
Ames, K. A.; Payne, L. E.
1995
A Phragmen-Lindelöf alternative for a class of quasilinear second order parabolic problems. Zbl 0833.35018
Lin, Changhao; Payne, L. E.
1995
Pointwise bounds and spatial decay estimates in heat conduction problems. Zbl 0849.35011
Payne, L. E.; Philippin, G. A.
1995
On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Zbl 0819.76077
Ames, K. A.; Payne, L. E.
1994
Some Phragmén-Lindelöf type results for the biharmonic equation. Zbl 0810.31001
Payne, L. E.; Schaefer, P. W.
1994
Phragmen-Lindelöf type results for second order quasilinear parabolic equations in $$\mathbb{R}^ 2$$. Zbl 0799.35124
Lin, Changhao; Payne, Lawrence E.
1994
On overdetermined boundary value problems for the biharmonic operator. Zbl 0810.35020
Payne, L. E.; Schaefer, P. W.
1994
The influence of domain and diffusivity perturbations on the decay of end effects in heat conduction. Zbl 0809.35034
Lin, Changhao; Payne, L. E.
1994
Continuous dependence results for solutions of the Navier-Stokes equations backward in time. Zbl 0814.35144
Ames, K. A.; Payne, L. E.
1994
Uniqueness and continuous dependence of solutions to a multidimensional thermoelastic contact problem. Zbl 0809.73055
Ames, K. A.; Payne, L. E.
1994
On gradient maximum principles for quasilinear elliptic equations. Zbl 0820.35018
Payne, L. E.; Philippin, G. A.
1994
Stabilizing the backward heat equation against errors in the initial time geometry. Zbl 0900.35042
Ames, K. A.; Payne, L. E.
1994
A Phragmén-Lindelöf principle for the equation of a surface of constant mean curvature. Zbl 0792.35066
Knops, R. J.; Payne, L. E.
1994
Spatial decay estimates in time-dependent Stokes flow. Zbl 0787.35060
Ames, K. A.; Payne, L. E.; Schaefer, P. W.
1993
Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions. Zbl 0790.31002
Horgan, C. O.; Payne, L. E.
1993
On the asymptotic behavior of solutions of linear second-order boundary- value problems on a semi-infinite strip. Zbl 0819.35014
Horgan, C. O.; Payne, L. E.
1993
...and 161 more Documents
all top 5

### Cited by 2,478 Authors

 118 Payne, Lawrence Edward 84 Quintanilla de Latorre, Ramón 65 Straughan, Brian 37 Philippin, Gérard A. 36 Knops, Robin J. 31 Schaefer, Philip W. 27 Saanouni, Tarek 27 Zhou, Jun 26 Xu, Runzhang 25 Ding, Juntang 24 Levine, Howard Allen 23 Repin, Sergeĭ Igorevich 23 Song, Jong Chul 22 Liu, Yan 19 Horgan, Cornelius Oliver 19 Lin, Changhao 19 Sperb, Rene P. 19 Vernier-Piro, Stella 19 Vohralík, Martin 18 Cheng, Qingming 18 Chiriţă, Stan 18 Zhang, Jian 17 Ames, Karen A. 16 Enache, Cristian 16 Fang, Zhongbo 16 Wang, Qiaoling 16 Xia, Changyu 15 Bandle, Catherine 15 Nguyen Huy Tuan 15 Ye, Yaojun 14 Ashbaugh, Mark S. 14 Ciarletta, Michele 13 Benguria, Rafael D. 13 Marin, Marin I. 13 Marras, Monica 12 Gazzola, Filippo 12 Han, Yuzhu 12 Hersch, Joseph 12 Leseduarte, Mari Carme 12 Li, Yuanfei 12 Rammaha, Mohammad A. 12 Ukhlov, Alexander Dadar-Oolovich 12 Viglialoro, Giuseppe 11 Bloom, Frederick 11 Esquivel-Avila, Jorge Alfredo 11 Kalantarov, Varga K. 11 Rionero, Salvatore 10 Dökmeci, M. Cengiz 10 Gol’dshtein, Vladimir Mikhailovich 10 Miranville, Alain M. 10 Shang, Yadong 10 Song, Xianfa 10 Trombetti, Cristina 10 Xu, Guangyu 10 Yamamoto, Masahiro 9 Fu, Chuli 9 Hill, Antony A. 9 Ibragimov, Akif 9 Liu, Wenjun 9 Mu, Chunlai 9 Nakanishi, Kenji 9 Nitsch, Carlo 9 Sun, Hejun 9 Trong, Dang Duc 9 Valdinoci, Enrico 8 Ding, Hang 8 Galdi, Giovanni Paolo 8 Gan, Zaihui 8 Iesan, Dorin 8 Kieu, Thinh Tri 8 Liu, Gongwei 8 Liu, Yacheng 8 Magnanini, Rolando 8 Mihăilescu, Mihai 8 Roseman, Joseph J. 8 Shen, Xuhui 8 Shu, Ji 8 Steinerberger, Stefan 8 Yang, Hongcang 8 Yang, Yanbing 7 Aulisa, Eugenio 7 Carasso, Alfred S. 7 Carstensen, Carsten 7 Chen, Daguang 7 Chen, Hua 7 Della Pietra, Francesco 7 Di, Huafei 7 Gavitone, Nunzia 7 Grossi, Massimo 7 Hoang, Luan Thach 7 Hon, Yiu-Chung 7 Kawohl, Bernd 7 Liang, Fei 7 Liu, Genqian 7 Matevosyan, Hovik A. 7 Poggesi, Giorgio 7 Wei, Ting 7 Xiong, Xiangtuan 6 Acker, Andrew F. 6 Ainsworth, Mark ...and 2,378 more Authors
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### Cited in 373 Serials

 193 Journal of Mathematical Analysis and Applications 138 ZAMP. Zeitschrift für angewandte Mathematik und Physik 106 Archive for Rational Mechanics and Analysis 90 Applicable Analysis 80 Journal of Differential Equations 77 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 63 Journal of Elasticity 56 Mathematical Methods in the Applied Sciences 50 International Journal of Engineering Science 49 Boundary Value Problems 45 Computers & Mathematics with Applications 43 Applied Mathematics and Computation 42 Calculus of Variations and Partial Differential Equations 39 Journal of Mathematical Physics 37 Transactions of the American Mathematical Society 33 Proceedings of the American Mathematical Society 32 Journal of Computational and Applied Mathematics 32 Applied Mathematics Letters 32 Nonlinear Analysis. Real World Applications 30 Journal of Functional Analysis 30 Nonlinear Analysis. Theory, Methods & Applications 26 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 24 Acta Mechanica 24 Journal of Mathematical Sciences (New York) 21 Annali di Matematica Pura ed Applicata. Serie Quarta 19 Computer Methods in Applied Mechanics and Engineering 19 Mathematics and Mechanics of Solids 18 Journal of Fluid Mechanics 17 Numerische Mathematik 16 Communications in Mathematical Physics 16 Communications in Partial Differential Equations 15 Acta Applicandae Mathematicae 15 The Journal of Geometric Analysis 15 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 15 Communications on Pure and Applied Analysis 14 Mathematische Annalen 13 Mathematics of Computation 13 Advances in Mathematics 13 Archiv der Mathematik 13 Meccanica 13 Quarterly of Applied Mathematics 13 Applied Numerical Mathematics 13 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 12 Journal of Computational Physics 12 Journal of Engineering Mathematics 12 Applied Mathematics and Optimization 12 Numerical Functional Analysis and Optimization 12 Zeitschrift für Analysis und ihre Anwendungen 12 Mathematical and Computer Modelling 12 Discrete and Continuous Dynamical Systems 12 Journal of Inequalities and Applications 12 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 12 Inverse Problems in Science and Engineering 11 Journal of Scientific Computing 11 Continuum Mechanics and Thermodynamics 11 Abstract and Applied Analysis 11 Mediterranean Journal of Mathematics 10 Journal d’Analyse Mathématique 10 Mathematical Notes 10 Duke Mathematical Journal 10 Mathematics and Computers in Simulation 10 SIAM Journal on Mathematical Analysis 10 Journal of Inverse and Ill-Posed Problems 10 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 10 Discrete and Continuous Dynamical Systems. Series B 10 Discrete and Continuous Dynamical Systems. Series S 10 Electronic Research Archive 9 Mathematische Zeitschrift 9 Ricerche di Matematica 9 SIAM Journal on Numerical Analysis 9 Applied Mathematics and Mechanics. (English Edition) 9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Acta Mathematicae Applicatae Sinica. English Series 9 Numerical Methods for Partial Differential Equations 9 Applied Mathematical Modelling 9 AIMS Mathematics 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Calcolo 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Communications in Contemporary Mathematics 8 Advances in Nonlinear Analysis 7 Mathematika 7 SIAM Journal on Scientific Computing 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Advances in Difference Equations 7 Evolution Equations and Control Theory 6 Journal of Applied Mathematics and Mechanics 6 Journal of the Franklin Institute 6 Automatica 6 Inventiones Mathematicae 6 Journal of the Mathematical Society of Japan 6 Manuscripta Mathematica 6 Mathematische Nachrichten 6 Rendiconti del Circolo Matemàtico di Palermo. Serie II 6 Results in Mathematics 6 Annals of Global Analysis and Geometry 6 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 6 Potential Analysis 6 Electronic Journal of Differential Equations (EJDE) ...and 273 more Serials
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### Cited in 51 Fields

 1,969 Partial differential equations (35-XX) 499 Mechanics of deformable solids (74-XX) 412 Fluid mechanics (76-XX) 316 Numerical analysis (65-XX) 151 Global analysis, analysis on manifolds (58-XX) 103 Operator theory (47-XX) 97 Calculus of variations and optimal control; optimization (49-XX) 96 Classical thermodynamics, heat transfer (80-XX) 95 Differential geometry (53-XX) 73 Potential theory (31-XX) 69 Biology and other natural sciences (92-XX) 65 Ordinary differential equations (34-XX) 61 Functional analysis (46-XX) 51 Real functions (26-XX) 32 Quantum theory (81-XX) 31 Probability theory and stochastic processes (60-XX) 30 Functions of a complex variable (30-XX) 28 Integral equations (45-XX) 28 Convex and discrete geometry (52-XX) 25 Statistical mechanics, structure of matter (82-XX) 24 Optics, electromagnetic theory (78-XX) 18 Dynamical systems and ergodic theory (37-XX) 17 Systems theory; control (93-XX) 15 Measure and integration (28-XX) 13 Special functions (33-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Mechanics of particles and systems (70-XX) 10 Geophysics (86-XX) 9 Information and communication theory, circuits (94-XX) 8 Operations research, mathematical programming (90-XX) 7 Combinatorics (05-XX) 7 Approximations and expansions (41-XX) 6 Integral transforms, operational calculus (44-XX) 6 Statistics (62-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Relativity and gravitational theory (83-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Difference and functional equations (39-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX)

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