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## Friedman, Avner

Compute Distance To:
 Author ID: friedman.avner Published as: Friedman, A.; Friedman, Avner External Links: MGP · Wikidata · GND
 Documents Indexed: 550 Publications since 1956, including 43 Books Biographic References: 1 Publication
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#### Co-Authors

 211 single-authored 43 Caffarelli, Luis Ángel 35 Hu, Bei 12 Chen, Xinfu 12 Velázquez, Juan J. L. 11 Reitich, Fernando 10 Alt, Hans Wilhelm 8 DiBenedetto, Emmanuele 8 McLeod, John Bryce 8 Yakubu, Abdul-Aziz 7 Fontelos López, Marco Antonio 7 Hao, Wenrui 6 Bazaliy, Borys V. 6 Cui, Shangbin 6 Kim, Yangjin 6 Ledzewicz, Urszula 6 Siewe, Nourridine 5 Anderson, Robert F. V. 5 Devinatz, Allen 5 Jensen, Robert E. 5 Lai, Xiulan 5 Pinsky, Mark Allan 5 Xue, Chuan 4 Bellout, Hamid 4 Bensoussan, Alain 4 Brézis, Haïm 4 Craciun, Gheorghe 4 Huang, Chaocheng 4 Kao, Chiu-Yen 4 Littman, Walter 4 Shinbrot, Marvin 4 Torelli, Alessandro 4 Turkington, Bruce E. 4 Vogelius, Michael S. 3 Aguda, Baltazar D. 3 Elliott, Charles M. 3 Herrero, Miguel Ángel 3 Huang, Shaoyun 3 Jiang, Lishang 3 Lacey, Andrew A. 3 Lam, King-Yeung 3 Liu, Yong 3 Ross, David Stuart 2 Baiocchi, Claudio 2 Bazaliy, Yaroslaw B. 2 Chen, Duan 2 Dembele, Bassidy 2 Elliott, Robert James 2 Evans, Lawrence Craig 2 Goel, Pranay 2 Green, J. Edward F. 2 Isakov, Victor M. 2 Jain, Harsh Vardhan 2 Kashdan, Eugene 2 Kaur, Balveen 2 Kinderlehrer, David 2 Lesinski, Gregory B. 2 Liao, Kang-Ling 2 Liu, Wenxiong 2 Lo, Wing-Cheong 2 Lungu, Edward M. 2 Marsh, Clay B. 2 Oswald, Luc 2 Ou, Biao 2 Pozzi, Gianni Arrigo 2 Satoskar, Abhay R 2 Schättler, Heinz Michael 2 Shih, Chih-Wen 2 Tao, Youshan 2 Tello, José Ignacio 2 Tzavaras, Athanasios E. 2 Véron, Laurent 2 Vogel, Thomas Irvin 2 Yong, Jiongmin 2 Zhang, Jianhua 1 Aronson, Donald G. 1 Arsenescu, Razvan I. 1 Bai, Xue-Feng 1 Banasiak, Jacek 1 Bao, Gang 1 Barbu, Viorel 1 Bassom, Andrew P. 1 Bell, Jonathan 1 Bemelmans, Josef 1 Bernis, Francisco 1 Borisovich, Andreĭ Yur’evich 1 Borisyuk, Alla 1 Boushaba, Khalid 1 Brokate, Martin 1 Brown, Anthony K. 1 Bruno, Oscar P. 1 Budd, Christopher John 1 Caligiuri, Michael A. 1 Chechkin, Gregory Aleksandrovich 1 Chiocca, E. Antonio 1 Chou, Ching-Shan 1 Conley, Elizabeth 1 Conwell, Darwin L. 1 Coskun, Huseyin 1 Crouser, Elliott D. 1 Day, Judy D. ...and 93 more Co-Authors
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#### Serials

 48 Journal of Differential Equations 46 Transactions of the American Mathematical Society 38 Archive for Rational Mechanics and Analysis 34 Indiana University Mathematics Journal 26 Journal of Mathematical Analysis and Applications 21 Journal of Mathematics and Mechanics 20 SIAM Journal on Mathematical Analysis 13 Mathematical Biosciences and Engineering 12 Bulletin of Mathematical Biology 12 Communications in Partial Differential Equations 12 Journal of Theoretical Biology 11 The IMA Volumes in Mathematics and its Applications 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 10 Pacific Journal of Mathematics 10 SIAM Journal on Control and Optimization 10 Nonlinear Analysis. Theory, Methods & Applications 8 Discrete and Continuous Dynamical Systems. Series B 7 SIAM Journal on Applied Mathematics 6 Journal of Mathematical Biology 5 Duke Mathematical Journal 5 Proceedings of the American Mathematical Society 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Proceedings of the National Academy of Sciences of the United States of America 5 Bulletin of the American Mathematical Society 4 Mathematical Biosciences 4 Journal of Functional Analysis 4 Journal für die Reine und Angewandte Mathematik 4 Kiberneticheskiĭ Sbornik. Novaya Seriya 4 European Journal of Applied Mathematics 4 Interfaces and Free Boundaries 3 Journal d’Analyse Mathématique 3 Acta Mathematica 3 Illinois Journal of Mathematics 3 Michigan Mathematical Journal 3 Notices of the American Mathematical Society 3 Lecture Notes in Mathematics 2 Communications on Pure and Applied Mathematics 2 American Journal of Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annales Polonici Mathematici 2 Mathematics of Operations Research 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Quarterly of Applied Mathematics 2 Asymptotic Analysis 2 SIAM Review 2 Discrete and Continuous Dynamical Systems 2 Multiscale Modeling & Simulation 2 Journal of Biological Dynamics 2 Mathematical Modelling of Natural Phenomena 2 Lecture Notes on Mathematical Modelling in the Life Sciences 2 Oxford Graduate Texts 1 Inverse Problems 1 Israel Journal of Mathematics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Reviews of Modern Physics 1 Rocky Mountain Journal of Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Applied Mathematics and Optimization 1 Journal of the Faculty of Science. Section I A 1 Journal of Optimization Theory and Applications 1 Chinese Annals of Mathematics. Series B 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Non-Newtonian Fluid Mechanics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Continuum Mechanics and Thermodynamics 1 Applied Mathematics. Series A (Chinese Edition) 1 Finance and Stochastics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales (España) 1 SIAM Journal on Control 1 Regional Conference Series in Mathematics 1 Mathematics in Industry 1 Networks and Heterogeneous Media 1 Science China. Mathematics 1 Philosophical Transactions A. Royal Society of London 1 CBMS Regional Conference Series in Mathematics 1 Springer Undergraduate Texts in Mathematics and Technology
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#### Fields

 310 Partial differential equations (35-XX) 125 Biology and other natural sciences (92-XX) 73 Fluid mechanics (76-XX) 68 Calculus of variations and optimal control; optimization (49-XX) 39 Probability theory and stochastic processes (60-XX) 33 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 28 Mechanics of deformable solids (74-XX) 26 General and overarching topics; collections (00-XX) 25 Systems theory; control (93-XX) 19 Optics, electromagnetic theory (78-XX) 18 Ordinary differential equations (34-XX) 16 Classical thermodynamics, heat transfer (80-XX) 12 Statistics (62-XX) 11 Operations research, mathematical programming (90-XX) 10 Potential theory (31-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Operator theory (47-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Integral equations (45-XX) 5 Numerical analysis (65-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

456 Publications have been cited 11,114 times in 8,197 Documents Cited by Year
Partial differential equations of parabolic type. Zbl 0144.34903
Friedman, A.
1964
Partial differential equations. Zbl 0224.35002
Friedman, Avner
1969
Stochastic differential equations and applications. Vol. 1. Zbl 0323.60056
Friedman, Avner
1975
Variational principles and free-boundary problems. Zbl 0564.49002
Friedman, Avner
1982
Blow-up of positive solutions of semilinear heat equations. Zbl 0576.35068
Friedman, Avner; McLeod, Bryce
1985
Stochastic differential equations and applications. Vol. 2. Zbl 0323.60057
Friedman, Avner
1976
Differential games. Zbl 0229.90060
Friedman, Avner
1971
Higher order nonlinear degenerate parabolic equations. Zbl 0702.35143
Bernis, Francisco; Friedman, Avner
1990
Variational problems with two phases and their free boundary. Zbl 0844.35137
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
Hölder estimates for non-linear degenerate parabolic systems. Zbl 0549.35061
DiBenedetto, Emmanuele; Friedman, Avner
1985
Classes of solutions of linear systems of partial differential equations of parabolic type. Zbl 0092.31002
Friedman, Avner
1957
Analysis of a mathematical model for the growth of tumors. Zbl 0944.92018
Friedman, Avner; Reitich, Fernando
1999
Nonlinear parabolic equations involving measures as initial conditions. Zbl 0527.35043
Brézis, Haïm; Friedman, Avner
1983
The Stefan problem in several space variables. Zbl 0162.41903
Friedman, A.
1968
Generalized functions and partial differential equations. Zbl 0116.07002
Friedman, A.
1963
Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065
Caffarelli, Luis A.; Friedman, Avner
1985
Variational principles and free-boundary problems. Reprint. Zbl 0671.49001
Friedman, Avner
1988
A free boundary problem arising in a model of wound healing. Zbl 0972.35193
Chen, Xinfu; Friedman, Avner
2000
Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions. Zbl 0631.35041
Friedman, Avner
1986
Regularity of the free boundary of a gas flow in an $$n$$-dimensional porous medium. Zbl 0439.76085
Caffarelli, Luis A.; Friedman, Avner
1980
Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth. Zbl 0983.35019
Friedman, Avner; Reitich, Fernando
2001
Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence. Zbl 0684.35087
Friedman, Avner; Vogelius, Michael
1989
Regularity of solutions of nonlinear degenerate parabolic systems. Zbl 0527.35038
DiBenedetto, Emmanuele; Friedman, Avner
1984
Blow-up of solutions of nonlinear degenerate parabolic equations. Zbl 0619.35060
Friedman, Avner; McLeod, Bryce
1986
Foundations of modern analysis. Zbl 0198.07601
Friedman, Avner
1970
Analysis of a mathematical model of the effect of inhibitors on the growth of tumors. Zbl 0998.92022
Cui, Shangbin; Friedman, Avner
2000
Foundations of modern analysis. Reprint of the 1970 orig. Zbl 0557.46001
Friedman, Avner
1982
The asymptotic behavior of gas in an $$n$$-dimensional porous medium. Zbl 0447.76076
Friedman, Avner; Kamin, Shoshana
1980
Parabolic variational inequalities in one space dimension and smoothness of the free boundary. Zbl 0295.35045
Friedman, Avner
1975
Optimal stochastic switching and the Dirichlet problem for the Bellman equation. Zbl 0425.35046
Evans, Lawrence C.; Friedman, Avner
1979
A one phase Stefan problem. Zbl 0334.49002
Friedman, Avner; Kinderlehrer, David
1975
Free boundary problems for parabolic equations. I: Melting of solids. Zbl 0089.07801
Friedman, Avner
1959
Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Zbl 1087.92039
Friedman, Avner; Hu, Bei
2006
Mathematical analysis of a model for the initiation of angiogenesis. Zbl 1020.35030
Fontelos, Marco A.; Friedman, Avner; Hu, Bei
2002
Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047
Caffarelli, Luis A.; Friedman, Avner
1985
Mathematical analysis and challenges arising from models of tumor growth. Zbl 1135.92013
Friedman, Avner
2007
Remarks on the maximum principle for parabolic equations and its applications. Zbl 0103.06403
Friedman, Avner
1958
A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
Volterra integral equations in Banach space. Zbl 0147.12302
Friedman, A.; Shinbrot, M.
1967
On the regularity of the solutions of nonlinear elliptic and parabolic systems of partial differential equations. Zbl 0078.27702
Friedman, Avner
1958
A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. Zbl 1054.35144
Chen, Xinfu; Friedman, Avner
2003
Determining cracks by boundary measurements. Zbl 0697.35165
Friedman, Avner; Vogelius, Michael
1989
The obstacle problem for the biharmonic operator. Zbl 0405.31007
Caffarelli, Luis A.; Friedman, Avner
1979
Stability of solutions of chemotaxis equations in reinforced random walks. Zbl 1025.35005
Friedman, Avner; Tello, J. Ignacio
2002
Analysis of a mathematical model of the growth of necrotic tumors. Zbl 0984.35169
Cui, Shangbin; Friedman, Avner
2001
Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060
Caffarelli, Luis A.; Friedman, Avner
1979
The boundary-value problem in domains with very rapidly oscillating boundary. Zbl 0938.35049
Chechkin, Gregory A.; Friedman, Avner; Piatnitski, Andrey L.
1999
Symmetry-breaking bifurcations of free boundary problems in three dimensions. Zbl 1054.35145
Fontelos, Marco A.; Friedman, Avner
2003
On the properties of a singular Sturm-Liouville equation determined by its spectral functions. Zbl 0091.08102
Friedman, Avner
1957
Stochastic differential equations and applications. Reprint of the 1975 and 1976 original editions. Zbl 1113.60003
Friedman, Avner
2006
Analysis of a mathematical model of tumor lymphangiogenesis. Zbl 1060.92036
Friedman, Avner; Lolas, Georgios
2005
A hierarchy of cancer models and their mathematical challenges. Zbl 1052.35094
Friedman, Avner
2004
A single point blow-up for solutions of semilinear parabolic systems. Zbl 0648.35042
Friedman, Avner; Giga, Yoshikazu
1987
Asymptotic stability for a free boundary problem arising in a tumor model. Zbl 1136.35106
Friedman, Avner; Hu, Bei
2006
The free boundary of a semilinear elliptic equation. Zbl 0552.35079
Friedman, Avner; Phillips, Daniel
1984
Stochastic differential games. Zbl 0208.39402
Friedman, Avner
1972
Partial differential equations of parabolic type. Zbl 0173.12701
Friedman, A.
1968
Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model. Zbl 1161.35059
Friedman, Avner; Hu, Bei
2008
A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Zbl 1031.35151
Bazaliy, Borys V.; Friedman, Avner
2003
The time-harmonic Maxwell equations in a doubly periodic structure. Zbl 0759.35046
Dobson, David; Friedman, Avner
1992
Extinction properties of semilinear heat equations with strong absorption. Zbl 0655.35050
Friedman, Avner; Herrero, Miguel A.
1987
The blow-up boundary for nonlinear wave equations. Zbl 0638.35053
Caffarelli, Luis A.; Friedman, Avner
1986
Bifurcation for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1136.35107
Friedman, Avner; Hu, Bei
2007
Optimal control for variational inequalities. Zbl 0604.49007
Friedman, Avner
1986
Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Zbl 0439.76084
Caffarelli, Luis A.; Friedman, Avner
1979
On integral equations of Volterra type. Zbl 0134.31502
Friedman, A.
1963
Nonlinear stability of a quasi-static Stefan problem with surface tension: a continuation approach. Zbl 1072.35208
Reitich, Fernando; Friedman, Avner
2001
The shape of axisymmetric rotating fluid. Zbl 0439.35068
Caffarelli, Luis A.; Friedman, Avner
1980
On the uniqueness in the inverse conductivity problem with one measurement. Zbl 0703.35165
Friedman, Avner; Isakov, Victor
1989
The ill-posed Hele-Shaw model and the Stefan problem for supercooled water. Zbl 0621.35102
DiBenedetto, Emmanuele; Friedman, Avner
1984
Asymptotic estimates for the plasma problem. Zbl 0466.35033
Caffarelli, Luis A.; Friedman, Avner
1980
Nonlinear variational inequalities and differential games with stopping times. Zbl 0297.90120
Bensoussan, Alain; Friedman, Avner
1974
Interior estimates for parabolic systems of partial differential equations. Zbl 0082.30402
Friedman, Avner
1958
Addendum to “Hölder estimates for nonlinear degenerate parabolic systems”. Zbl 0595.35065
DiBenedetto, Emmanuelle; Friedman, Avner
1985
Differentiability of the blow-up curve for one dimensional nonlinear wave equations. Zbl 0593.35055
Caffarelli, Luis A.; Friedman, Avner
1985
Jets with two fluids. I. One free boundary. Zbl 0551.76013
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
Reinforcement problems for elliptic equations and variational inequalities. Zbl 0434.35079
Brézis, Haïm; Caffarelli, Luis A.; Friedman, Avner
1980
Systems of nonlinear wave equations with nonlinear viscosity. Zbl 0685.35070
Friedman, Avner; Nečas, Jindřich
1988
Axially symmetric jet flows. Zbl 0515.76017
Alt, H. W.; Caffarelli, L. A.; Friedman, A.
1983
Nonzero-sum stochastic differential games with stopping times and free boundary problems. Zbl 0368.93029
Bensoussan, Alain; Friedman, Avner
1977
Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Zbl 1089.35079
Bazaliy, Borys; Friedman, Avner
2003
A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Zbl 1036.34018
Cui, Shangbin; Friedman, Avner
2003
Maxwell’s equations in a periodic structure. Zbl 0727.35131
Chen, Xinfu; Friedman, Avner
1991
Analysis of a free-boundary tumor model with angiogenesis. Zbl 1344.35172
Friedman, Avner; Lam, King-Yeung
2015
Asymmetric jet flows. Zbl 0515.76018
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1982
Vortex rings: existence and asymptotic estimates. Zbl 0497.76031
Friedman, Avner; Turkington, Bruce
1981
Blow-up of solutions of nonlinear heat equations. Zbl 0653.35038
Caffarelli, Luis A.; Friedman, Avner
1988
Optimal control for parabolic variational inequalities. Zbl 0624.49005
Friedman, Avner
1987
One dimensional Stefan problems with nonmonotone free boundary. Zbl 0162.42001
Friedman, A.
1968
Isometric embedding of riemannian manifolds into Euclidean spaces. Zbl 0137.14901
Friedman, A.
1965
Generalized heat transfer between solids and gases under nonlinear boundary conditions. Zbl 0101.31102
Friedman, Avner
1959
Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1122.35013
Friedman, Avner; Hu, Bei
2007
Compressible flows of jets and cavities. Zbl 0614.76074
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1985
Stochastic games and variational inequalities. Zbl 0285.90089
Friedman, Avner
1973
On the existence of spatially patterned dormant malignancies in a model for the growth of non-necrotic vascular tumors. Zbl 1013.92024
Friedman, Avner; Reitich, Fernando
2001
Asymptotic behavior of solutions of $$u_ t=\Delta u^ m$$ as $$m\to \infty$$. Zbl 0651.35039
Caffarelli, Luis A.; Friedman, Avner
1987
Periodic behaviour for the evolutionary dam problem and related free boundary problems. Zbl 0624.35084
DiBenedetto, Emmanuele; Friedman, Avner
1986
Jets with two fluids. II: Two free boundaries. Zbl 0588.76017
Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner
1984
Convexity of the free boundary in the Stefan problem and in the dam problem. Zbl 0375.35028
Friedman, Avner; Jensen, Robert
1977
Analyticity of the free boundary for the Stefan problem. Zbl 0329.35034
Friedman, Avner
1976
Mathematical modeling in scheduling cancer treatment with combination of VEGF inhibitor and chemotherapy drugs. Zbl 1406.92312
Lai, Xiulan; Friedman, Avner
2019
Rheumatoid arthritis – a mathematical model. Zbl 1406.92273
Moise, Nicolae; Friedman, Avner
2019
The role of exosomes in pancreatic cancer microenvironment. Zbl 1394.92056
Friedman, Avner; Hao, Wenrui
2018
Mathematical model of chronic pancreatitis. Zbl 1404.92096
Hao, Wenrui; Komar, Hannah M.; Hart, Phil A.; Conwell, Darwin L.; Lesinski, Gregory B.; Friedman, Avner
2017
The role of TNF-$$\alpha$$ inhibitor in glioma virotherapy: a mathematical model. Zbl 1362.92034
Ratajczyk, Elzbieta; Ledzewicz, Urszula; Leszczynski, Maciej; Friedman, Avner
2017
Granuloma formation in leishmaniasis: a mathematical model. Zbl 1368.92087
Siewe, Nourridine; Yakubu, Abdul-Aziz; Satoskar, Abhay R; Friedman, Avner
2017
Mathematical modeling of liver fibrosis. Zbl 1348.92079
Friedman, Avner; Hao, Wenrui
2017
Free boundary problems for systems of Stokes equations. Zbl 1357.35298
Friedman, Avner
2016
Immune response to infection by Leishmania: a mathematical model. Zbl 1341.92042
Siewe, Nourridine; Yakubu, Abdul-Aziz; Satoskar, Abhay R.; Friedman, Avner
2016
Introduction to mathematical biology. Modeling, analysis, and simulations. Zbl 1351.92001
Chou, Ching-Shan; Friedman, Avner
2016
Analysis of a free-boundary tumor model with angiogenesis. Zbl 1344.35172
Friedman, Avner; Lam, King-Yeung
2015
A mathematical model of atherosclerosis with reverse cholesterol transport and associated risk factors. Zbl 1334.92198
Friedman, Avner; Hao, Wenrui
2015
A free boundary problem for steady small plaques in the artery and their stability. Zbl 1322.35181
Friedman, Avner; Hao, Wenrui; Hu, Bei
2015
Free boundary problems in biology. Zbl 1353.35291
Friedman, Avner
2015
Effects of CCN1 and macrophage content on glioma virotherapy: a mathematical model. Zbl 1335.92040
Jacobsen, Karly; Russell, Luke; Kaur, Balveen; Friedman, Avner
2015
A PDE model for the dynamics of trail formation by ants. Zbl 1311.35325
Fontelos, Marco A.; Friedman, Avner
2015
A mathematical model for pancreatic cancer growth and treatments. Zbl 1412.92154
Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B.; Friedman, Avner
2014
Mathematical model of sarcoidosis. Zbl 1355.92049
Hao, Wenrui; Crouser, Elliott D.; Friedman, Avner
2014
On a multiphase multicomponent model of biofilm growth. Zbl 1288.35388
Friedman, Avner; Hu, Bei; Xue, Chuan
2014
Mathematical modeling of biological processes. Zbl 1302.92004
Friedman, Avner; Kao, Chiu-Yen
2014
On the stability of steady states in a granuloma model. Zbl 1288.35482
Friedman, Avner; Lam, King-Yeung
2014
A Bovine babesiosis model with dispersion. Zbl 1282.92019
Friedman, Avner; Yakubu, Abdul-Aziz
2014
Mathematical model of renal interstitial fibrosis. Zbl 1355.92050
Hao, Wenrui; Rovin, Brad H.; Friedman, Avner
2014
Modulation of the camp response by $$\mathrm{G}\alpha _i$$ and $$\mathrm{G}\beta \gamma$$: a computational study of G protein signaling in immune cells. Zbl 1298.92038
Leander, R.; Friedman, A.
2014
Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Zbl 1277.92013
Jain, Harsh Vardhan; Friedman, Avner
2013
Anthrax epizootic and migration: persistence or extinction. Zbl 1303.92116
Friedman, Avner; Yakubu, Abdul-Aziz
2013
A two-phase free boundary problem with discontinuous velocity: Application to tumor model. Zbl 1256.35208
Chen, Duan; Friedman, Avner
2013
Epidemiological models with seasonality. Zbl 1345.92140
Friedman, Avner
2013
Mathematical methods and models in biomedicine. Zbl 1254.92046
Ledzewicz, Urszula (ed.); Schättler, Heinz (ed.); Friedman, Avner (ed.); Kashdan, Eugene (ed.)
2013
Mathematical model of the roles of T cells in inflammatory bowel disease. Zbl 1272.92030
Lo, Wing-Cheong; Arsenescu, Razvan I.; Friedman, Avner
2013
The role of CD200-CD200R in tumor immune evasion. Zbl 1330.92024
Liao, Kang-Ling; Bai, Xue-Feng; Friedman, Avner
2013
The diffusion approximation for linear nonautonomous reaction-hyperbolic equations. Zbl 1276.35014
Friedman, Avner; Hu, Bei; Keener, James P.
2013
A mathematical model for cell-induced gel compaction in vitro. Zbl 1257.92018
Green, J. E. F.; Bassom, Andrew P.; Friedman, Avner
2013
Host demographic Allee effect, fatal disease, and migration: persistence or extinction. Zbl 1273.34052
Friedman, Avner; Yakubu, Abdul-Aziz
2012
PDE problems arising in mathematical biology. Zbl 1260.49001
Friedman, Avner
2012
Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model. Zbl 1267.92043
Chen, Duan; Roda, Julie M.; Marsh, Clay B.; Eubank, Timothy D.; Friedman, Avner
2012
Modeling the inhibition of breast cancer growth by GM-CSF. Zbl 1337.92118
Szomolay, Barbara; Eubank, Tim D.; Roberts, Ryan D.; Marsh, Clay B.; Friedman, Avner
2012
A three dimensional model of wound healing: analysis and computation. Zbl 1395.92076
Friedman, Avner; Hu, Bei; Xue, Chuan
2012
Cancer as multifaceted disease. Zbl 1241.92038
Friedman, A.
2012
Conservation laws in mathematical biology. Zbl 1258.35142
Friedman, Avner
2012
Asymptotic limit in a cell differentiation model with consideration of transcription. Zbl 1267.34078
Friedman, Avner; Kao, Chiu-Yen; Shih, Chih-Wen
2012
Fatal disease and demographic Allee effect: population persistence and extinction. Zbl 1447.92337
Friedman, Avner; Yakubu, Abdul-Aziz
2012
A mathematical model for chronic wounds. Zbl 1259.92043
Friedman, Avner; Xue, Chuan
2011
Asymptotic analysis for the narrow escape problem. Zbl 1252.35030
Chen, Xinfu; Friedman, Avner
2011
Tumor cells proliferation and migration under the influence of their microenvironment. Zbl 1259.92042
Friedman, Avner; Kim, Yangjin
2011
Modeling the host response to inhalation anthrax. Zbl 1405.92143
Day, Judy; Friedman, Avner; Schlesinger, Larry S.
2011
Analysis of a mathematical model of ischemic cutaneous wounds. Zbl 1217.35195
Friedman, Avner; Hu, Bei; Xue, Chuan
2010
Interaction of tumor with its micro-environment: a mathematical model. Zbl 1197.92027
Kim, Yangjin; Friedman, Avner
2010
Mathematical model for optimal use of sulfadoxine-pyrimethamine as a temporary malaria vaccine. Zbl 1191.92025
Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz
2010
Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments. Zbl 1204.92041
Kim, Yangjin; Wallace, Julie; Li, Fu; Ostrowski, Michael; Friedman, Avner
2010
Cell cycle control at the first restriction point and its effect on tissue growth. Zbl 1202.92024
Friedman, Avner; Hu, Bei; Kao, Chiu-Yen
2010
Mathematical modeling of preadipocyte fate determination. Zbl 1406.92145
Coskun, Huseyin; Summerfield, Taryn L. S.; Kniss, Douglas A.; Friedman, Avner
2010
A mathematical model for pattern formation of glioma cells outside the tumor spheroid core. Zbl 1405.92032
Kim, Yangjin; Lawler, Sean; Nowicki, Michal O.; Chiocca, E. Antonio; Friedman, Avner
2009
Free boundary problems associated with multiscale tumor models. Zbl 1172.35080
Friedman, A.
2009
Malaria model with periodic mosquito birth and death rates. Zbl 1342.92232
Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz
2009
Asymptotic phases in a cell differentiation model. Zbl 1173.35590
Friedman, Avner; Kao, Chiu-Yen; Shih, Chih-Wen
2009
Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model. Zbl 1161.35059
Friedman, Avner; Hu, Bei
2008
A multiscale tumor model. Zbl 1157.35501
Friedman, Avner
2008
Models of cellular regulation. Zbl 1231.92030
Aguda, Baltazar D.; Friedman, Avner
2008
The role of oxygen in tissue maintenance: mathematical modeling and qualitive analysis. Zbl 1152.35524
Friedman, Avner; Hu, Bei
2008
Tutorials in mathematical biosciences IV. Evolution and ecology. Tutorials presented at the Mathematical Bioscience Institute (MBI) in the years 2005–2006. Zbl 1130.92002
Friedman, Avner (ed.)
2008
The extensional flow of a thin sheet of incompressible, transversely isotropic fluid. Zbl 1141.76009
Green, J. Edward F.; Friedman, Avner
2008
A parabolic-hyperbolic quasilinear system. Zbl 1158.35004
Chen, Xinfu; Friedman, Avner; Hu, Bei
2008
Mathematical analysis and challenges arising from models of tumor growth. Zbl 1135.92013
Friedman, Avner
2007
Bifurcation for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1136.35107
Friedman, Avner; Hu, Bei
2007
Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1122.35013
Friedman, Avner; Hu, Bei
2007
Uniform convergence for approximate traveling waves in linear reaction-hyperbolic systems. Zbl 1133.35006
Friedman, Avner; Hu, Bei
2007
Uniform convergence for approximate traveling waves in linear reaction-diffusion-hyperbolic systems. Zbl 1132.35006
Friedman, Avner; Hu, Bei
2007
One-dimensional free boundary problem for actin-based propulsion of Listeria. Zbl 1104.92016
Bazaliy, Borys; Bazaliy, Yaroslaw; Friedman, Avner
2007
Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Zbl 1087.92039
Friedman, Avner; Hu, Bei
2006
Stochastic differential equations and applications. Reprint of the 1975 and 1976 original editions. Zbl 1113.60003
Friedman, Avner
2006
Asymptotic stability for a free boundary problem arising in a tumor model. Zbl 1136.35106
Friedman, Avner; Hu, Bei
2006
A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth. Zbl 1106.35145
Friedman, Avner
2006
Approximate traveling waves in linear reaction-hyperbolic equations. Zbl 1147.35330
Friedman, Avner; Craciun, Gheorghe
2006
Homogenization of the cell cytoplasm: the calcium bidomain equations. Zbl 1128.35303
Goel, Pranay; Sneyd, James; Friedman, Avner
2006
Tutorials in mathematical biosciences III. Cell cycle, prolifereation, and cancer. Zbl 1122.92030
Friedman, Avner (ed.)
2006
Differential games. Reprint of the 1971 original ed. Zbl 1225.91011
Friedman, Avner
2006
Analysis of a mathematical model of tumor lymphangiogenesis. Zbl 1060.92036
Friedman, Avner; Lolas, Georgios
2005
Borisovich, Andrei; Friedman, Avner
2005
A hyperbolic free boundary problem modeling tumor growth: asymptotic behavior. Zbl 1082.35166
Chen, Xinfu; Cui, Shangbin; Friedman, Avner
2005
A model of intracellular transport of particles in an axon. Zbl 1068.92016
Friedman, Avner; Craciun, Gheorghe
2005
Generalized functions and partial differential equations. Reprint of the 1963 original. Zbl 1121.46001
Friedman, Avner
2005
The Hele-Shaw problem with surface tension in a half-plane: a model problem. Zbl 1075.76022
Bazaliy, Borys V.; Friedman, Avner
2005
The Hele-Shaw problem with surface tension in a half-plane. Zbl 1076.76028
Bazaliy, Borys V.; Friedman, Avner
2005
Tutorials in mathematical biosciences. I: Mathematical neuroscience. Zbl 1062.92008
Borisyuk, Alla; Ermentrout, Bard G.; Friedman, Avner; Terman, David
2005
Friedman, Avner
2005
Free boundary problems with surface tension conditions. Zbl 1153.35409
Friedman, Avner
2005
Mathematical analysis of a modular network coordinating the cell cycle and apoptosis. Zbl 1079.92023
Craciun, Gheorghe; Aguda, Baltazar; Friedman, Avner
2005
A hierarchy of cancer models and their mathematical challenges. Zbl 1052.35094
Friedman, Avner
2004
Symmetry-breaking bifurcations of charged drops. Zbl 1094.76022
Fontelos, Marco A.; Friedman, Avner
2004
Free boundary problems arising in tumor models. Zbl 1162.35460
Friedman, Avner
2004
A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. Zbl 1054.35144
Chen, Xinfu; Friedman, Avner
2003
Symmetry-breaking bifurcations of free boundary problems in three dimensions. Zbl 1054.35145
Fontelos, Marco A.; Friedman, Avner
2003
A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Zbl 1031.35151
Bazaliy, Borys V.; Friedman, Avner
2003
Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Zbl 1089.35079
Bazaliy, Borys; Friedman, Avner
2003
A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Zbl 1036.34018
Cui, Shangbin; Friedman, Avner
2003
A hyperbolic free boundary problem modeling tumor growth. Zbl 1040.35143
Cui, Shangbin; Friedman, Avner
2003
Nonlinear stability of the Muskat problem with capillary pressure at the free boundary. Zbl 1028.35123
Friedman, Avner; Tao, Youshan
2003
Analysis of a model of a virus that replicates selectively in tumor cells. Zbl 1052.92027
Friedman, Avner; Tao, Youshan
2003
Mathematical models in photographic science. Zbl 1290.82030
Friedman, Avner; Ross, David S.
2003
...and 356 more Documents
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#### Cited by 7,867 Authors

 204 Friedman, Avner 56 Mu, Chunlai 52 Vazquez, Juan Luis 47 Hu, Bei 47 Winkler, Michael 39 Caffarelli, Luis Ángel 37 Zheng, Sining 35 Galaktionov, Victor Aleksandrovich 34 Shahgholian, Henrik 34 Wang, Mingxin 34 Yi, Fahuai 32 Cui, Shangbin 30 Mao, Xuerong 30 Xu, Shihe 29 Pao, Chia-Ven 29 Tao, Youshan 28 Cannon, John Rozier 28 Liu, Bingchen 26 Chen, Xinfu 26 Lin, Zhigui 25 Fasano, Antonio 24 Li, Fengjie 24 Primicerio, Mario 23 Ammari, Habib M. 23 Peletier, Lambertus Adrianus 22 Diaz Diaz, Jesus Ildefonso 22 Du, Lili 22 Guo, Jong-Shenq 20 Souplet, Philippe 20 Xie, Chunhong 19 Herrero, Miguel Ángel 19 Macías-Díaz, Jorge Eduardo 19 Rossi, Julio Daniel 19 Shen, Wenxian 19 Velázquez, Juan J. L. 18 Aronson, Donald G. 18 Du, Yihong 18 Véron, Laurent 17 Hayashi, Nakao 17 Yin, Hongming 17 Zheng, Pan 16 Bao, Gang 16 Gao, Wenjie 16 Karatzas, Ioannis 16 Lions, Pierre-Louis 16 Yong, Jiongmin 16 Zaag, Hatem 15 Bertsch, Michiel 15 Bögelein, Verena 15 DiBenedetto, Emmanuele 15 Ding, Juntang 15 Escher, Joachim 15 Kamin, Shoshana 15 Kang, Hyeonbae 15 Mingione, Giuseppe 15 Rodríguez-Bernal, Aníbal 15 Taranets, Roman M. 15 Valdinoci, Enrico 15 Yin, Jingxue 14 Chechkin, Gregory Aleksandrovich 14 Ishige, Kazuhiro 14 Perthame, Benoît 14 Tello, José Ignacio 14 Weiss, Georg Sebastian 14 Wu, Junde 13 Amann, Herbert 13 Cheng, Jianfeng 13 Hao, Wenrui 13 Karakhanyan, Aram L. 13 Le, Dung 13 Lenhart, Suzanne M. 13 Prüß, Jan Wilhelm 13 Qi, Yuanwei 13 Salsa, Sandro 13 Suzuki, Takashi 13 Tarzia, Domingo Alberto 13 Tesei, Alberto 13 Zhang, Xicheng 12 Alessandrini, Giovanni 12 Ambrazevičius, Algirdas 12 Balachandran, Krishnan 12 Bandle, Catherine 12 Bellomo, Nicola 12 Fila, Marek 12 Guo, Boling 12 Kim, Kwang Ik 12 Lee, Ki-Ahm 12 Lesnic, Daniel 12 Pascucci, Andrea 12 Vasylyeva, Nataliya V. 12 Wang, Liangchen 12 Yang, Zhou 11 Barron, Emmanuel Nicholas 11 Beretta, Elena 11 Denisov, Vasiliĭ Nikolaevich 11 Elliott, Robert James 11 Fernández-Cara, Enrique 11 Fitzgibbon, William Edward 11 Gol’dman, Nataliya L’vovna 11 Hu, Guanghui ...and 7,767 more Authors
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#### Cited in 601 Serials

 592 Journal of Mathematical Analysis and Applications 564 Journal of Differential Equations 242 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 234 Nonlinear Analysis. Theory, Methods & Applications 206 Archive for Rational Mechanics and Analysis 191 Transactions of the American Mathematical Society 144 Communications in Partial Differential Equations 119 Journal of Functional Analysis 110 Applicable Analysis 110 Applied Mathematics and Computation 106 Annali di Matematica Pura ed Applicata. Serie Quarta 102 Nonlinear Analysis. Real World Applications 93 Calculus of Variations and Partial Differential Equations 91 Journal of Computational and Applied Mathematics 91 Stochastic Processes and their Applications 89 Proceedings of the American Mathematical Society 85 Computers & Mathematics with Applications 84 Mathematical Methods in the Applied Sciences 82 Applied Mathematics and Optimization 81 Journal of Optimization Theory and Applications 72 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 71 Journal of Mathematical Sciences (New York) 70 ZAMP. Zeitschrift für angewandte Mathematik und Physik 68 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 66 Discrete and Continuous Dynamical Systems. Series B 61 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 61 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 59 Journal de Mathématiques Pures et Appliquées. Neuvième Série 59 SIAM Journal on Mathematical Analysis 58 Journal of Mathematical Biology 57 Mathematische Zeitschrift 55 Discrete and Continuous Dynamical Systems 51 Mathematische Annalen 50 Stochastic Analysis and Applications 49 Communications in Mathematical Physics 44 Applied Mathematics Letters 43 The Annals of Applied Probability 43 Boundary Value Problems 42 Bulletin of Mathematical Biology 39 Mathematics of Computation 39 Advances in Mathematics 39 Journal of Theoretical Biology 38 Probability Theory and Related Fields 38 European Journal of Applied Mathematics 37 Journal of Mathematical Physics 37 Numerische Mathematik 37 Mathematical and Computer Modelling 36 Stochastics 36 NoDEA. Nonlinear Differential Equations and Applications 35 Siberian Mathematical Journal 33 Journal d’Analyse Mathématique 33 Journal of Computational Physics 33 Manuscripta Mathematica 33 Journal of Dynamics and Differential Equations 32 Systems & Control Letters 32 Journal of Evolution Equations 31 Acta Applicandae Mathematicae 30 Mathematical Biosciences 29 Ukrainian Mathematical Journal 28 Israel Journal of Mathematics 28 Mathematical Notes 28 Communications on Pure and Applied Analysis 27 Computer Methods in Applied Mechanics and Engineering 27 Numerical Functional Analysis and Optimization 27 Bulletin of the American Mathematical Society 26 Automatica 26 Czechoslovak Mathematical Journal 26 Rendiconti del Seminario Matematico della Università di Padova 26 SIAM Journal on Control and Optimization 26 Physica D 25 The Annals of Probability 25 Journal of Economic Theory 25 Differential Equations 24 Publications of the Research Institute for Mathematical Sciences, Kyoto University 24 Quarterly of Applied Mathematics 24 Journal of Economic Dynamics & Control 24 Comptes Rendus. Mathématique. Académie des Sciences, Paris 23 Communications on Pure and Applied Mathematics 23 Zeitschrift für Analysis und ihre Anwendungen 23 Applied Numerical Mathematics 23 Acta Mathematicae Applicatae Sinica. English Series 22 Journal of Applied Mathematics and Mechanics 22 Rocky Mountain Journal of Mathematics 22 SIAM Journal on Applied Mathematics 22 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 21 International Journal of Control 21 Duke Mathematical Journal 21 Journal of Soviet Mathematics 21 Journal of Scientific Computing 21 The Journal of Geometric Analysis 21 Potential Analysis 21 Doklady Mathematics 20 Applied Mathematical Modelling 20 Acta Mathematica Sinica. English Series 20 Discrete and Continuous Dynamical Systems. Series S 20 Science China. Mathematics 19 Acta Mathematica 19 Advances in Difference Equations 19 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 18 Chinese Annals of Mathematics. Series B ...and 501 more Serials
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#### Cited in 58 Fields

 5,467 Partial differential equations (35-XX) 1,047 Probability theory and stochastic processes (60-XX) 970 Biology and other natural sciences (92-XX) 849 Fluid mechanics (76-XX) 773 Numerical analysis (65-XX) 745 Calculus of variations and optimal control; optimization (49-XX) 609 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 474 Systems theory; control (93-XX) 462 Ordinary differential equations (34-XX) 358 Operator theory (47-XX) 320 Mechanics of deformable solids (74-XX) 256 Classical thermodynamics, heat transfer (80-XX) 224 Integral equations (45-XX) 185 Dynamical systems and ergodic theory (37-XX) 167 Global analysis, analysis on manifolds (58-XX) 156 Functional analysis (46-XX) 147 Statistical mechanics, structure of matter (82-XX) 134 Optics, electromagnetic theory (78-XX) 130 Potential theory (31-XX) 128 Differential geometry (53-XX) 104 Operations research, mathematical programming (90-XX) 96 Statistics (62-XX) 66 Real functions (26-XX) 61 Quantum theory (81-XX) 41 Computer science (68-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 36 Information and communication theory, circuits (94-XX) 34 Measure and integration (28-XX) 34 Geophysics (86-XX) 32 Approximations and expansions (41-XX) 29 Difference and functional equations (39-XX) 25 Astronomy and astrophysics (85-XX) 24 Mechanics of particles and systems (70-XX) 23 Integral transforms, operational calculus (44-XX) 21 Functions of a complex variable (30-XX) 20 Relativity and gravitational theory (83-XX) 14 General and overarching topics; collections (00-XX) 13 Convex and discrete geometry (52-XX) 13 General topology (54-XX) 11 Several complex variables and analytic spaces (32-XX) 10 Special functions (33-XX) 8 History and biography (01-XX) 8 Topological groups, Lie groups (22-XX) 8 Manifolds and cell complexes (57-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Nonassociative rings and algebras (17-XX) 7 Abstract harmonic analysis (43-XX) 6 Combinatorics (05-XX) 5 Number theory (11-XX) 5 Algebraic topology (55-XX) 4 Group theory and generalizations (20-XX) 3 Algebraic geometry (14-XX) 3 Geometry (51-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Associative rings and algebras (16-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX)

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