Edit Profile (opens in new tab) Payne, Lawrence Edward (b. 1923 d. 2011) Co-Author Distance 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 · IdRef 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 1,061 Co-Co-Authors all top 5 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 Mond, Bertram 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 all top 5 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 Springer Tracts in Natural Philosophy 1 Journal of Rational Mechanics and Analysis all top 5 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 265 Publications have been cited 5,315 times in 3,219 Documents Cited by ▼ Year ▼ Saddle points and instability of nonlinear hyperbolic equations. Zbl 0317.35059 Payne, L. E.; Sattinger, D. H. 521 1976 An optimal Poincaré inequality for convex domains. Zbl 0099.08402 Payne, L. E.; Weinberger, H. F. 336 1960 Improperly posed problems in partial differential equations. Zbl 0302.35003 Payne, L. E. 158 1975 On the ratio of consecutive eigenvalues. Zbl 0073.08203 Payne, Laurent E.; Pólya, George; Weinberger, Hans F. 146 1956 Isoperimetric inequalities and their applications. Zbl 0154.12602 Payne, L. E. 138 1967 Uniqueness theorems in linear elasticity. Zbl 0224.73016 Knops, R. J.; Payne, L. E. 108 1971 Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Zbl 1110.35031 Payne, L. E.; Schaefer, P. W. 98 2007 Lower bounds for blow-up time in parabolic problems under Neumann conditions. Zbl 1110.35032 Payne, L. E.; Schaefer, P. W. 84 2006 Convergence and continuous dependence for the Brinkman-Forchheimer equations. Zbl 1136.76448 Payne, L. E.; Straughan, B. 79 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. 68 1998 Decay estimates for the constrained elastic cylinder of variable cross section. Zbl 0706.73015 Flavin, J. N.; Knops, R. J.; Payne, L. E. 65 1989 New bounds for solutions of second order elliptic partial differential equations. Zbl 0093.10901 Payne, L. E.; Weinberger, H. F. 63 1958 Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Zbl 0933.76091 Payne, L. E.; Song, J. C.; Straughan, B. 62 1999 Blow-up phenomena for some nonlinear parabolic problems. Zbl 1159.35382 Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 61 2008 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 61 2010 On inequalities of Korn, Friedrichs and Babuska-Aziz. Zbl 0512.73017 Horgan, C. O.; Payne, L. E. 58 1983 The Stokes flow problem for a class of axially symmetric bodies. Zbl 0091.42202 Payne, L. E.; Pell, W. H. 56 1960 Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Zbl 1184.35077 Payne, L. E.; Schaefer, P. W. 51 2009 Spatial decay estimates in transient heat conduction. Zbl 0553.35037 Horgan, C. O.; Payne, L. E.; Wheeler, L. T. 51 1984 Duality theorems in some overdetermined boundary value problems. Zbl 0698.35051 Payne, L. E.; Schaefer, Philip W. 48 1989 Bounds for blow-up time in nonlinear parabolic problems. Zbl 1139.35055 Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 47 2008 Energy bounds in dynamical problems for a semi-infinite elastic beam. Zbl 0736.73035 Flavin, J. N.; Knops, R. J.; Payne, L. E. 46 1990 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. 45 2010 Some isoperimetric inequalities for membrane frequencies and torsional rigidity. Zbl 0098.39201 Payne, L. E.; Weinberger, H. F. 45 1961 Some isoperimetric inequalities for harmonic functions. Zbl 0199.16902 Payne, L. E. 45 1970 Lower bounds for blow-up time in a nonlinear parabolic problem. Zbl 1177.35043 Payne, L. E.; Song, J. C. 43 2009 Some inequalities for Stekloff eigenvalues. Zbl 0315.35069 Hersch, J.; Payne, L. E.; Schiffer, M. M. 43 1974 On the mean value of the fundamental mode in the fixed membrane problem. Zbl 0323.35057 Payne, L. E.; Stakgold, I. 43 1973 Sur le quotient de deux fréquences propres consécutives. Zbl 0065.08801 Payne, Laurent E.; Pólya, George; Weinberger, Hans F. 42 1955 Bounds in the Cauchy problem for the Laplace equation. Zbl 0094.29801 Payne, L. E. 42 1960 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. 41 1979 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. 41 1974 Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics. Zbl 0227.35017 Knops, R. J.; Payne, L. E. 41 1971 Effect of anisotropic permeability on Darcy’s law. Zbl 0984.76024 Payne, L. E.; Rodrigues, J. F.; Straughan, B. 39 2001 Continuous data dependence for the equations of classical elastodynamics. Zbl 0184.51004 Knops, R. J.; Payne, L. E. 39 1969 On two conjectures in the fixed membrane eigenvalue problem. Zbl 0272.35058 Payne, Lawrence E. 39 1973 Structural stability for the Darcy equations of flow in porous media. Zbl 0912.76088 Payne, L. E.; Straughan, B. 38 1998 Inequalities for eigenvalues of membranes and plates. Zbl 0064.34802 Payne, L. E. 37 1955 On Korn’s inequality. Zbl 0107.31105 Payne, L. E.; Weinberger, H. F. 36 1961 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. 35 1996 Some applications of the maximum principle in the problem of torsional creep. Zbl 0378.73028 Payne, L. E.; Philippin, G. A. 34 1977 Decay estimates in steady pipe flow. Zbl 0675.76029 Ames, K. A.; Payne, L. E. 32 1989 On the stability of solutions of Navier-Stokes equations backward in time. Zbl 0159.14201 Knops, R. J.; Payne, L. E. 31 1968 Lower bounds for vibration frequencies of elastically supportes membranes and plates. Zbl 0083.19406 Payne, L. E.; Weinberger, H. F. 31 1957 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. 31 1981 An isoperimetric inequality for the first eigenfunction in the fixed membrane problem. Zbl 0241.73080 Payne, Lawrence E.; Rayner, Margaret E. 31 1972 Nonlinear problems in nuclear reactor analysis. Zbl 0259.35025 Stakgold, I.; Payne, L. E. 30 1973 Lower bounds for blow-up in a model of chemotaxis. Zbl 1231.35027 Payne, L. E.; Song, J. C. 30 2012 Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Zbl 0982.35119 Ames, K. A.; Payne, L. E. 28 1998 Some remarks on maximum principles. Zbl 0334.35029 Payne, L. E. 28 1976 On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity. Zbl 0209.56605 Knops, R. J.; Payne, L. E. 27 1970 Structural stability for a Brinkman fluid. Zbl 1208.35011 Lin, Changhao; Payne, L. E. 26 2007 Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid. Zbl 0681.76013 Payne, L. E.; Straughan, B. 26 1989 Decay, growth, continuous dependence and uniqueness results in generalized heat conduction theories. Zbl 0694.35007 Morro, A.; Payne, L. E.; Straughan, B. 26 1990 Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Zbl 1277.35075 Payne, L. E.; Philippin, G. A. 25 2013 Blow-up in parabolic problems under Robin boundary conditions. Zbl 1156.35408 Payne, L. E.; Schaefer, P. W. 25 2008 Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Zbl 0893.76090 Payne, L. E.; Song, J. C. 25 1997 New bounds in harmonic and biharmonic problems. Zbl 0064.09903 Payne, L. E.; Weinberger, H. F. 25 1955 Analysis of convective reaction-diffusion equation. II. Zbl 0702.35126 Levine, H. A.; Payne, L. E.; Sacks, P. E.; Straughan, B. 24 1989 New isoperimetric inequalities for eigenvalues and other physical quantities. Zbl 0074.31405 Payne, L. E. 23 1956 Bounds for eigenvalues and eigenvectors of symmetric operators. Zbl 0159.44204 Moler, C. B.; Payne, L. E. 22 1968 Extreme principles and isoperimetric inequalities for some mixed problems of Stekloff’s type. Zbl 0165.12603 Hersch, J.; Payne, L. E. 22 1968 Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. Zbl 1139.35085 Lin, Changhao; Payne, L. E. 22 2008 Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints. Zbl 0293.35004 Levine, H. A.; Payne, L. E. 22 1974 Energy and pointwise bounds in some non-standard parabolic problems. Zbl 1056.35104 Ames, K. A.; Payne, L. E.; Schaefer, P. W. 22 2004 Uniqueness in classical elastodynamics. Zbl 0159.56201 Knops, R. J.; Payne, L. E. 21 1967 On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Zbl 0819.76077 Ames, K. A.; Payne, L. E. 21 1994 Improved estimates for continuous data dependence in linear elastodynamics. Zbl 0663.73009 Knops, R. J.; Payne, L. E. 20 1988 Structural stability for the Brinkman equations of flow in double diffusive convection. Zbl 1167.35435 Lin, Changhao; Payne, L. E. 20 2007 Stability in linear elasticity. Zbl 0182.58905 Knops, R. J.; Payne, L. E. 20 1968 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. 20 2012 Convection in thawing subsea permafrost. Zbl 0645.76055 Galdi, G. P.; Payne, L. E.; Proctor, M. R. E.; Straughan, B. 19 1987 Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Zbl 1136.35318 Payne, L. E.; Straughan, B. 19 2000 Spatial decay estimates in time-dependent Stokes flow. Zbl 0787.35060 Ames, K. A.; Payne, L. E.; Schaefer, P. W. 19 1993 Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions. Zbl 0790.31002 Horgan, C. O.; Payne, L. E. 19 1993 Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Zbl 0928.35015 Ames, K. A.; Payne, L. E. 19 1999 Decay estimates for second-order quasilinear partial differential equations. Zbl 0556.35053 Horgan, C. O.; Payne, L. E. 19 1984 On two free boundary problems in potential theory. Zbl 0760.31003 Payne, L. E.; Philippin, G. A. 18 1991 Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows. Zbl 0970.76097 Payne, L. E.; Song, J. C. 18 2000 Uniqueness criteria for steady state solutions of the Navier-Stokes equations. Zbl 0149.44605 Payne, L. E. 18 1965 Some Phragmén-Lindelöf type results for the biharmonic equation. Zbl 0810.31001 Payne, L. E.; Schaefer, P. W. 18 1994 Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Zbl 1241.35027 Payne, L. E.; Philippin, G. A. 18 2012 Note on a lemma of Finn and Gilbar. Zbl 0078.40002 Payne, L. E.; Weinberger, H. F. 18 1957 Decay estimates for a class of nonlinear boundary value problems in two dimensions. Zbl 0678.35027 Horgan, C. O.; Payne, L. E. 17 1989 Bounds in the Neumann problem for second order uniformly elliptic operators. Zbl 0111.09701 Bramble, J. H.; Payne, L. E. 17 1962 On some maximum principles involving harmonic functions and their derivatives. Zbl 0402.35014 Payne, L. E.; Philippin, G. A. 17 1979 Some non-standard problems in viscous flow. Zbl 1174.76307 Payne, L. E.; Schaefer, P. W.; Song, J. C. 17 2004 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. 17 1992 Some inequalities for vector functions with applications in elasticity. Zbl 0109.16806 Bramble, J. H.; Payne, L. E. 17 1962 On a priori bounds in the Cauchy problem for elliptic equations. Zbl 0199.16603 Payne, L. E. 17 1970 Spatial decay bounds in the channel flow of an incompressible viscous fluid. Zbl 1185.35024 Lin, Changhao; Payne, Lawrence E. 16 2004 Some isoperimetric norm bounds for solutions of the Helmholtz equation. Zbl 0256.35023 Payne, Lawrence E.; Rayner, Margaret E. 16 1973 Some general remarks on improperly posed problems for partial differential equations. Zbl 0257.35079 Payne, L. E. 16 1973 A Saint-Venant principle for nonlinear elasticity. Zbl 0519.73005 Knops, R. J.; Payne, L. E. 16 1983 Decay bounds for solutions of second order parabolic problems and their derivatives. Zbl 0832.35019 Payne, L. E.; Philippin, G. A. 15 1995 Energy bounds for some nonstandard problems in partial differential equations. Zbl 1121.35331 Payne, L. E.; Schaefer, P. W. 15 2002 Isoperimetric inequalities in the torsion and clamped membrane problems for convex plane domains. Zbl 0521.73056 Payne, L. E.; Philippin, G. A. 14 1983 Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function. Zbl 0481.35022 Payne, L. E. 14 1981 Unconditional nonlinear stability in penetrative convection. Zbl 0709.76048 Payne, L. E.; Straughan, B. 13 1987 On stabilizing ill-posed problems against errors in geometry and modeling. Zbl 0658.35086 Payne, L. E. 13 1987 Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Zbl 1277.35075 Payne, L. E.; Philippin, G. A. 25 2013 Lower bounds for blow-up in a model of chemotaxis. Zbl 1231.35027 Payne, L. E.; Song, J. C. 30 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. 20 2012 Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Zbl 1241.35027 Payne, L. E.; Philippin, G. A. 18 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 61 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. 45 2010 Blow-up and decay criteria for a model of chemotaxis. Zbl 1195.35058 Payne, L. E.; Song, J. C. 7 2010 Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Zbl 1184.35077 Payne, L. E.; Schaefer, P. W. 51 2009 Lower bounds for blow-up time in a nonlinear parabolic problem. Zbl 1177.35043 Payne, L. E.; Song, J. C. 43 2009 Decay for a Keller-Segel chemotaxis model. Zbl 1180.35529 Payne, L. E.; Straughan, B. 8 2009 An ill-posed problem for the heat equation. Zbl 1179.35339 Payne, L. E.; Philippin, G. A. 1 2009 Blow-up phenomena for some nonlinear parabolic problems. Zbl 1159.35382 Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 61 2008 Bounds for blow-up time in nonlinear parabolic problems. Zbl 1139.35055 Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 47 2008 Blow-up in parabolic problems under Robin boundary conditions. Zbl 1156.35408 Payne, L. E.; Schaefer, P. W. 25 2008 Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. Zbl 1139.35085 Lin, Changhao; Payne, L. E. 22 2008 Blow-up phenomena for some nonlinear parabolic systems. Zbl 1169.35340 Payne, L. E.; Schaefer, P. W. 9 2008 Spatial decay bounds for double diffusive convection in Brinkman flow. Zbl 1133.35021 Payne, L. E.; Song, J. C. 8 2008 Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Zbl 1110.35031 Payne, L. E.; Schaefer, P. W. 98 2007 Structural stability for a Brinkman fluid. Zbl 1208.35011 Lin, Changhao; Payne, L. E. 26 2007 Structural stability for the Brinkman equations of flow in double diffusive convection. Zbl 1167.35435 Lin, Changhao; Payne, L. E. 20 2007 Lower bounds for the blow-up time in a temperature dependent Navier-Stokes flow. Zbl 1124.35057 Payne, L. E.; Song, J. C. 12 2007 Spatial decay in a double diffusive convection problem in Darcy flow. Zbl 1110.76051 Payne, L. E.; Song, J. C. 11 2007 A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov. Zbl 1136.35110 Payne, L. E. 11 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. 6 2007 Spatial decay in a cross-diffusion problem. Zbl 1134.35018 Payne, L. E.; Song, J. C. 1 2007 Lower bounds for blow-up time in parabolic problems under Neumann conditions. Zbl 1110.35032 Payne, L. E.; Schaefer, P. W. 84 2006 On a proposed model for heat conduction. Zbl 1126.80003 Payne, L. E.; Song, J. C. 10 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 6 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. 6 2006 Continuous dependence inequalities for a class of quasilinear parabolic problems. Zbl 1100.35013 Payne, L. E.; Philippin, G. A.; Safoui, A. 1 2006 Some nonstandard problems in generalized heat conduction. Zbl 1080.35034 Payne, L. E.; Schaefer, P. W.; Song, J. C. 10 2005 Alternative spatial growth and decay for constrained motion in an elastic cylinder. Zbl 1074.74009 Knops, R. J.; Payne, L. E. 9 2005 Improved spatial decay bounds in generalized heat conduction. Zbl 1082.35078 Payne, L. E.; Song, J. C. 6 2005 On two classes of nonstandard parabolic problems. Zbl 1083.35132 Ames, K. A.; Payne, L. E.; Song, J. C. 3 2005 Spatial decay bounds for a class of quasi-linear parabolic initial-boundary value problems. Zbl 1349.35173 Payne, L. E.; Philippin, G. A. 2 2005 Energy and pointwise bounds in some non-standard parabolic problems. Zbl 1056.35104 Ames, K. A.; Payne, L. E.; Schaefer, P. W. 22 2004 Some non-standard problems in viscous flow. Zbl 1174.76307 Payne, L. E.; Schaefer, P. W.; Song, J. C. 17 2004 Spatial decay bounds in the channel flow of an incompressible viscous fluid. Zbl 1185.35024 Lin, Changhao; Payne, Lawrence E. 16 2004 Spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid. Zbl 1075.35054 Lin, Changhao; Payne, Lawrence E. 13 2004 On a nonstandard problem for heat conduction in a cylinder. Zbl 1052.35066 Ames, K. A.; Payne, L. E.; Schaefer, P. W. 11 2004 Decay bounds for solutions of second order parabolic problems and their derivatives. III. Zbl 1072.35097 Payne, L. E.; Philippin, G. A. 7 2004 Decay bounds for solutions of second order parabolic problems and their derivatives. II. Zbl 1069.35506 Payne, L. E.; Philippin, G. A. 6 2004 Continuous dependence of heat flux on spatial geometry for the generalized Maxwell-Cattaneo system. Zbl 1054.35007 Lin, Changhao; Payne, L. E. 5 2004 Improved bounds for some nonstandard problems in generalized heat conduction. Zbl 1065.35081 Payne, L. E.; Schaefer, P. W.; Song, J. C. 3 2004 Temporal decay bounds in generalized heat conduction. Zbl 1058.35142 Payne, L. E.; Song, J. C. 1 2004 Spatial decay estimates for the Maxwell-Cattaneo equations with mixed boundary conditions. Zbl 1065.35134 Payne, L. E.; Song, J. C. 1 2004 Energy bounds for some nonstandard problems in partial differential equations. Zbl 1121.35331 Payne, L. E.; Schaefer, P. W. 15 2002 Spatial decay bounds for the Forchheimer equations. Zbl 1211.76119 Payne, L. E.; Song, J. C. 9 2002 Decay bounds in initial-boundary value problems for nonlinear parabolic systems. Zbl 1011.35072 Payne, L. E.; Schaefer, P. W. 2 2002 Growth and decay in generalized thermoelasticity. Zbl 1211.74076 Payne, L. E.; Song, J. C. 2 2002 Effect of anisotropic permeability on Darcy’s law. Zbl 0984.76024 Payne, L. E.; Rodrigues, J. F.; Straughan, B. 39 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. 6 2001 Continuous dependence on spatial geometry for the generalized Maxwell-Cattaneo system. Zbl 0994.35024 Lin, Changhao; Payne, L. E. 3 2001 Eigenvalue and eigenfunction inequalities for the elastically supported membrane. Zbl 0986.35081 Payne, L. E.; Schaefer, P. W. 2 2001 Convergence results for generalized heat condution as the relaxation time tends to zero. Zbl 0977.35015 Payne, L. E.; Song, J. C. 1 2001 Continuous dependence on base data in an elastic prismatic cylinder. Zbl 1034.74007 Knops, R. J.; Payne, L. E. 1 2001 Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Zbl 1136.35318 Payne, L. E.; Straughan, B. 19 2000 Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows. Zbl 0970.76097 Payne, L. E.; Song, J. C. 18 2000 A naturally efficient numerical technique for porous convection stability with non-trivial boundary conditions. Zbl 0977.76070 Payne, L. E.; Straughan, B. 4 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. 4 2000 Saint-Venant type decay results for ill-posed elliptic problems. Zbl 1034.35144 Ames, Karen A.; Payne, Lawrence E. 1 2000 Convergence and continuous dependence for the Brinkman-Forchheimer equations. Zbl 1136.76448 Payne, L. E.; Straughan, B. 79 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. 62 1999 Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Zbl 0928.35015 Ames, K. A.; Payne, L. E. 19 1999 Convergence of the equations for a Maxwell fluid. Zbl 1136.76310 Payne, L. E.; Straughan, B. 13 1999 Effect of errors in the spatial geometry for temperature dependent Stokes flow. Zbl 0935.76020 Payne, L. E.; Straughan, B. 12 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. 9 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. 68 1998 Structural stability for the Darcy equations of flow in porous media. Zbl 0912.76088 Payne, L. E.; Straughan, B. 38 1998 Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Zbl 0982.35119 Ames, K. A.; Payne, L. E. 28 1998 Bounds and decay results for some second-order semilinear elliptic problems. Zbl 0917.35036 Payne, L. E.; Schaefer, P. W.; Song, J. C. 2 1998 Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Zbl 0893.76090 Payne, L. E.; Song, J. C. 25 1997 Continuous dependence results for a problem in penetrative convection. Zbl 0892.35079 Ames, Karen A.; Payne, Lawrence E. 8 1997 Continuous dependence on the initial-time geometry in generalized heat conduction. Zbl 0871.35013 Payne, L. E.; Song, J. C. 8 1997 Saint-Venant’s principle in linear isotropic elasticity for incompressible or nearly incompressible materials. Zbl 0907.73010 Horgan, C. O.; Payne, L. E. 7 1997 Continuous dependence on initial-time and spatial geometry in generalized heat conduction. Zbl 0889.35011 Payne, L. E.; Song, J. C. 6 1997 Continuous dependence results for an ill-posed problem in nonlinear viscoelasticity. Zbl 0906.73030 Ames, Karen A.; Payne, Lawrence E. 2 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. 1 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. 35 1996 Phragmén-Lindelöf and continuous dependence type results in generalized heat conduction. Zbl 0864.35051 Payne, L. E.; Song, J. C. 13 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. 4 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. 2 1996 A special class of maximum principles with applications to nonlinear boundary value problems. Zbl 0845.35013 Payne, L. E. 1 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. 1 1996 Decay bounds for solutions of second order parabolic problems and their derivatives. Zbl 0832.35019 Payne, L. E.; Philippin, G. A. 15 1995 Continuous dependence on initial-time geometry for a thermoelastic system with sign-indefinite elasticities. Zbl 0857.35128 Ames, K. A.; Payne, L. E. 12 1995 A Phragmen-Lindelöf alternative for a class of quasilinear second order parabolic problems. Zbl 0833.35018 Lin, Changhao; Payne, L. E. 8 1995 Pointwise bounds and spatial decay estimates in heat conduction problems. Zbl 0849.35011 Payne, L. E.; Philippin, G. A. 6 1995 On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Zbl 0819.76077 Ames, K. A.; Payne, L. E. 21 1994 Some Phragmén-Lindelöf type results for the biharmonic equation. Zbl 0810.31001 Payne, L. E.; Schaefer, P. W. 18 1994 On overdetermined boundary value problems for the biharmonic operator. Zbl 0810.35020 Payne, L. E.; Schaefer, P. W. 10 1994 Phragmen-Lindelöf type results for second order quasilinear parabolic equations in \(\mathbb{R}^ 2\). Zbl 0799.35124 Lin, Changhao; Payne, Lawrence E. 9 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. 9 1994 Continuous dependence results for solutions of the Navier-Stokes equations backward in time. Zbl 0814.35144 Ames, K. A.; Payne, L. E. 8 1994 Uniqueness and continuous dependence of solutions to a multidimensional thermoelastic contact problem. Zbl 0809.73055 Ames, K. A.; Payne, L. E. 7 1994 On gradient maximum principles for quasilinear elliptic equations. Zbl 0820.35018 Payne, L. E.; Philippin, G. A. 4 1994 Stabilizing the backward heat equation against errors in the initial time geometry. Zbl 0900.35042 Ames, K. A.; Payne, L. E. 2 1994 A Phragmén-Lindelöf principle for the equation of a surface of constant mean curvature. Zbl 0792.35066 Knops, R. J.; Payne, L. E. 1 1994 Spatial decay estimates in time-dependent Stokes flow. Zbl 0787.35060 Ames, K. A.; Payne, L. E.; Schaefer, P. W. 19 1993 Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions. Zbl 0790.31002 Horgan, C. O.; Payne, L. E. 19 1993 ...and 165 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,955 Authors 119 Payne, Lawrence Edward 91 Quintanilla de Latorre, Ramón 72 Straughan, Brian 39 Knops, Robin J. 37 Philippin, Gérard A. 35 Zhou, Jun 31 Schaefer, Philip W. 31 Xu, Runzhang 30 Saanouni, Tarek 28 Ding, Juntang 26 Repin, Sergeĭ Igorevich 24 Levine, Howard Allen 23 Liu, Yan 23 Song, Jong Chul 21 Chiriţă, Stan 21 Fang, Zhongbo 20 Lin, Changhao 20 Vernier-Piro, Stella 19 Horgan, Cornelius Oliver 19 Li, Yuanfei 19 Sperb, Rene P. 19 Vohralík, Martin 19 Xia, Changyu 19 Zhang, Jian 18 Cheng, Qingming 18 Wang, Qiaoling 17 Ames, Karen A. 17 Ciarletta, Michele 17 Enache, Cristian 17 Ye, Yaojun 16 Bandle, Catherine 16 Marin, Marin I. 16 Nguyen Huy Tuan 15 Ashbaugh, Mark S. 15 Ukhlov, Alexander Dadar-Oolovich 14 Han, Yuzhu 14 Marras, Monica 13 Benguria, Rafael D. 13 Leseduarte, Mari Carme 13 Rammaha, Mohammad A. 13 Viglialoro, Giuseppe 13 Yamamoto, Masahiro 12 Bloom, Frederick 12 Esquivel-Avila, Jorge Alfredo 12 Gazzola, Filippo 12 Gol’dshtein, Vladimir Mikhailovich 12 Grossi, Massimo 12 Hersch, Joseph 12 Kalantarov, Varga K. 12 Poggesi, Giorgio 12 Rionero, Salvatore 11 Chen, Hua 11 Li, Fengjie 11 Song, Xianfa 11 Trong, Dang Duc 11 Xu, Guangyu 11 Zhang, Hongwei 10 Carstensen, Carsten 10 Ding, Hang 10 Dökmeci, M. Cengiz 10 Liu, Gongwei 10 Miranville, Alain M. 10 Shang, Yadong 10 Steinerberger, Stefan 10 Sun, Hejun 10 Trombetti, Cristina 10 Valdinoci, Enrico 10 Yang, Yanbing 10 Zeng, Lingzhong 9 Fu, Chuli 9 Hill, Antony A. 9 Kieu, Thinh Tri 9 Liu, Wenjun 9 Magnanini, Rolando 9 Matevosyan, Hovik A. 9 Mihăilescu, Mihai 9 Mu, Chunlai 9 Nakanishi, Kenji 9 Nitsch, Carlo 9 Pchelintsev, Valery Anatol’evich 9 Shen, Xuhui 8 Bucur, Dorin 8 Chen, Daguang 8 Di, Huafei 8 Galdi, Giovanni Paolo 8 Gan, Zaihui 8 Gavitone, Nunzia 8 Hoang, Luan Thach 8 Ibragimov, Akif 8 Iesan, Dorin 8 Liu, Yacheng 8 Öchsner, Andreas 8 Roseman, Joseph J. 8 Shu, Ji 8 Yang, Hongcang 7 Ainsworth, Mark 7 Carasso, Alfred S. 7 Cheng, Jin 7 Della Pietra, Francesco 7 Girouard, Alexandre ...and 2,855 more Authors all top 5 Cited in 420 Serials 207 Journal of Mathematical Analysis and Applications 146 ZAMP. 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Matematica e Applicazioni 7 Electronic Journal of Differential Equations (EJDE) 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Taiwanese Journal of Mathematics 7 Journal of Mathematical Fluid Mechanics 7 Journal of Dynamical and Control Systems ...and 320 more Serials all top 5 Cited in 52 Fields 2,326 Partial differential equations (35-XX) 552 Mechanics of deformable solids (74-XX) 480 Fluid mechanics (76-XX) 381 Numerical analysis (65-XX) 183 Global analysis, analysis on manifolds (58-XX) 125 Differential geometry (53-XX) 122 Operator theory (47-XX) 120 Calculus of variations and optimal control; optimization (49-XX) 112 Classical thermodynamics, heat transfer (80-XX) 88 Potential theory (31-XX) 74 Biology and other natural sciences (92-XX) 73 Functional analysis (46-XX) 70 Ordinary differential equations (34-XX) 62 Real functions (26-XX) 44 Quantum theory (81-XX) 40 Functions of a complex variable (30-XX) 40 Probability theory and stochastic processes (60-XX) 34 Convex and discrete geometry (52-XX) 33 Optics, electromagnetic theory (78-XX) 31 Integral equations (45-XX) 27 Statistical mechanics, structure of matter (82-XX) 25 Dynamical systems and ergodic theory (37-XX) 24 Systems theory; control (93-XX) 18 Measure and integration (28-XX) 14 Special functions (33-XX) 14 Geophysics (86-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 11 Combinatorics (05-XX) 11 Approximations and expansions (41-XX) 11 Statistics (62-XX) 11 Mechanics of particles and systems (70-XX) 11 Information and communication theory, circuits (94-XX) 10 Operations research, mathematical programming (90-XX) 9 Integral transforms, operational calculus (44-XX) 6 Computer science (68-XX) 4 History and biography (01-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Difference and functional equations (39-XX) 4 Geometry (51-XX) 4 Relativity and gravitational theory (83-XX) 3 Number theory (11-XX) 2 General and overarching topics; collections (00-XX) 2 General topology (54-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Algebraic geometry (14-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) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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