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 1,035 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 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 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 261 Publications have been cited 4,845 times in 2,914 Documents Cited by ▼ Year ▼ Saddle points and instability of nonlinear hyperbolic equations. Zbl 0317.35059Payne, L. E.; Sattinger, D. H. 448 1976 An optimal Poincaré inequality for convex domains. Zbl 0099.08402Payne, L. E.; Weinberger, H. F. 290 1960 Improperly posed problems in partial differential equations. Zbl 0302.35003Payne, L. E. 145 1975 Isoperimetric inequalities and their applications. Zbl 0154.12602Payne, L. E. 134 1967 On the ratio of consecutive eigenvalues. Zbl 0073.08203Payne, Laurent E.; Pólya, George; Weinberger, Hans F. 134 1956 Uniqueness theorems in linear elasticity. Zbl 0224.73016Knops, R. J.; Payne, L. E. 101 1971 Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Zbl 1110.35031Payne, L. E.; Schaefer, P. W. 91 2007 Lower bounds for blow-up time in parabolic problems under Neumann conditions. Zbl 1110.35032Payne, L. E.; Schaefer, P. W. 80 2006 Convergence and continuous dependence for the Brinkman-Forchheimer equations. Zbl 1136.76448Payne, L. E.; Straughan, B. 70 1999 Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. Zbl 0906.35067Payne, L. E.; Straughan, B. 64 1998 New bounds for solutions of second order elliptic partial differential equations. Zbl 0093.10901Payne, L. E.; Weinberger, H. F. 60 1958 Decay estimates for the constrained elastic cylinder of variable cross section. Zbl 0706.73015Flavin, J. N.; Knops, R. J.; Payne, L. E. 59 1989 Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Zbl 0933.76091Payne, L. E.; Song, J. C.; Straughan, B. 55 1999 On inequalities of Korn, Friedrichs and Babuska-Aziz. Zbl 0512.73017Horgan, C. O.; Payne, L. E. 55 1983 Blow-up phenomena for some nonlinear parabolic problems. Zbl 1159.35382Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 55 2008 Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II. Zbl 1198.35131Payne, L. E.; Philippin, G. A.; Piro, S. Vernier 53 2010 The Stokes flow problem for a class of axially symmetric bodies. Zbl 0091.42202Payne, L. E.; Pell, W. H. 53 1960 Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Zbl 1184.35077Payne, L. E.; Schaefer, P. W. 48 2009 Spatial decay estimates in transient heat conduction. Zbl 0553.35037Horgan, C. O.; Payne, L. E.; Wheeler, L. T. 47 1984 Bounds for blow-up time in nonlinear parabolic problems. Zbl 1139.35055Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 43 2008 Lower bounds for blow-up time in a nonlinear parabolic problem. Zbl 1177.35043Payne, L. E.; Song, J. C. 42 2009 Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. I. Zbl 1227.35173Payne, L. E.; Philippin, G. A.; Vernier Piro, S. 42 2010 On the mean value of the fundamental mode in the fixed membrane problem. Zbl 0323.35057Payne, L. E.; Stakgold, I. 42 1973 Some isoperimetric inequalities for membrane frequencies and torsional rigidity. Zbl 0098.39201Payne, L. E.; Weinberger, H. F. 42 1961 Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elasto- dynamics. Zbl 0292.35067Knops, R. J.; Levine, H. A.; Payne, L. E. 41 1974 Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature. Zbl 0408.35015Payne, L. E.; Philippin, G. A. 41 1979 Duality theorems in some overdetermined boundary value problems. Zbl 0698.35051Payne, L. E.; Schaefer, Philip W. 40 1989 Some isoperimetric inequalities for harmonic functions. Zbl 0199.16902Payne, L. E. 40 1970 Bounds in the Cauchy problem for the Laplace equation. Zbl 0094.29801Payne, L. E. 40 1960 Sur le quotient de deux fréquences propres consécutives. Zbl 0065.08801Payne, Laurent E.; Pólya, George; Weinberger, Hans F. 39 1955 Some inequalities for Stekloff eigenvalues. Zbl 0315.35069Hersch, J.; Payne, L. E.; Schiffer, M. M. 38 1974 On two conjectures in the fixed membrane eigenvalue problem. Zbl 0272.35058Payne, Lawrence E. 38 1973 Energy bounds in dynamical problems for a semi-infinite elastic beam. Zbl 0736.73035Flavin, J. N.; Knops, R. J.; Payne, L. E. 37 1990 Structural stability for the Darcy equations of flow in porous media. Zbl 0912.76088Payne, L. E.; Straughan, B. 36 1998 Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics. Zbl 0227.35017Knops, R. J.; Payne, L. E. 36 1971 On Korn’s inequality. Zbl 0107.31105Payne, L. E.; Weinberger, H. F. 35 1961 Inequalities for eigenvalues of membranes and plates. Zbl 0064.34802Payne, L. E. 34 1955 Some applications of the maximum principle in the problem of torsional creep. Zbl 0378.73028Payne, L. E.; Philippin, G. A. 33 1977 Effect of anisotropic permeability on Darcy’s law. Zbl 0984.76024Payne, L. E.; Rodrigues, J. F.; Straughan, B. 33 2001 Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media. Zbl 0848.76089Payne, L. E.; Straughan, B. 32 1996 Continuous data dependence for the equations of classical elastodynamics. Zbl 0184.51004Knops, R. J.; Payne, L. E. 31 1969 Lower bounds for vibration frequencies of elastically supportes membranes and plates. Zbl 0083.19406Payne, L. E.; Weinberger, H. F. 30 1957 Decay estimates in steady pipe flow. Zbl 0675.76029Ames, K. A.; Payne, L. E. 28 1989 Lower bounds for blow-up in a model of chemotaxis. Zbl 1231.35027Payne, L. E.; Song, J. C. 28 2012 An isoperimetric inequality for the first eigenfunction in the fixed membrane problem. Zbl 0241.73080Payne, Lawrence E.; Rayner, Margaret E. 28 1972 Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Zbl 0982.35119Ames, K. A.; Payne, L. E. 27 1998 Some remarks on maximum principles. Zbl 0334.35029Payne, L. E. 26 1976 On the stability of solutions of Navier-Stokes equations backward in time. Zbl 0159.14201Knops, R. J.; Payne, L. E. 26 1968 Structural stability for a Brinkman fluid. Zbl 1208.35011Lin, Changhao; Payne, L. E. 25 2007 On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity. Zbl 0209.56605Knops, R. J.; Payne, L. E. 25 1970 New bounds in harmonic and biharmonic problems. Zbl 0064.09903Payne, L. E.; Weinberger, H. F. 25 1955 Blow-up in parabolic problems under Robin boundary conditions. Zbl 1156.35408Payne, L. E.; Schaefer, P. W. 24 2008 Analysis of convective reaction-diffusion equation. II. Zbl 0702.35126Levine, H. A.; Payne, L. E.; Sacks, P. E.; Straughan, B. 24 1989 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 0508.73051Acker, A.; Payne, L. E.; Philippin, G. 24 1981 Decay, growth, continuous dependence and uniqueness results in generalized heat conduction theories. Zbl 0694.35007Morro, A.; Payne, L. E.; Straughan, B. 23 1990 Energy and pointwise bounds in some non-standard parabolic problems. Zbl 1056.35104Ames, K. A.; Payne, L. E.; Schaefer, P. W. 23 2004 Nonlinear problems in nuclear reactor analysis. Zbl 0259.35025Stakgold, I.; Payne, L. E. 23 1973 Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Zbl 1277.35075Payne, L. E.; Philippin, G. A. 23 2013 Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Zbl 0893.76090Payne, L. E.; Song, J. C. 22 1997 New isoperimetric inequalities for eigenvalues and other physical quantities. Zbl 0074.31405Payne, L. E. 22 1956 On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Zbl 0819.76077Ames, K. A.; Payne, L. E. 20 1994 Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. Zbl 1139.35085Lin, Changhao; Payne, L. E. 20 2008 Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints. Zbl 0293.35004Levine, H. A.; Payne, L. E. 20 1974 Bounds for eigenvalues and eigenvectors of symmetric operators. Zbl 0159.44204Moler, C. B.; Payne, L. E. 20 1968 Extreme principles and isoperimetric inequalities for some mixed problems of Stekloff’s type. Zbl 0165.12603Hersch, J.; Payne, L. E. 20 1968 Structural stability for the Brinkman equations of flow in double diffusive convection. Zbl 1167.35435Lin, Changhao; Payne, L. E. 19 2007 Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid. Zbl 0681.76013Payne, L. E.; Straughan, B. 19 1989 Decay estimates for second-order quasilinear partial differential equations. Zbl 0556.35053Horgan, C. O.; Payne, L. E. 19 1984 Uniqueness in classical elastodynamics. Zbl 0159.56201Knops, R. J.; Payne, L. E. 19 1967 Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Zbl 1136.35318Payne, L. E.; Straughan, B. 19 2000 Convection in thawing subsea permafrost. Zbl 0645.76055Galdi, G. P.; Payne, L. E.; Proctor, M. R. E.; Straughan, B. 18 1987 Improved estimates for continuous data dependence in linear elastodynamics. Zbl 0663.73009Knops, R. J.; Payne, L. E. 18 1988 Spatial decay estimates in time-dependent Stokes flow. Zbl 0787.35060Ames, K. A.; Payne, L. E.; Schaefer, P. W. 18 1993 Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions. Zbl 1255.35059Payne, L. E.; Philippin, G. A. 18 2012 Stability in linear elasticity. Zbl 0182.58905Knops, R. J.; Payne, L. E. 18 1968 Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions. Zbl 0790.31002Horgan, C. O.; Payne, L. E. 17 1993 Decay estimates for a class of nonlinear boundary value problems in two dimensions. Zbl 0678.35027Horgan, C. O.; Payne, L. E. 17 1989 Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows. Zbl 0970.76097Payne, L. E.; Song, J. C. 17 2000 Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Zbl 0928.35015Ames, K. A.; Payne, L. E. 17 1999 Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Zbl 1241.35027Payne, L. E.; Philippin, G. A. 17 2012 Some non-standard problems in viscous flow. Zbl 1174.76307Payne, L. E.; Schaefer, P. W.; Song, J. C. 17 2004 On some maximum principles involving harmonic functions and their derivatives. Zbl 0402.35014Payne, L. E.; Philippin, G. A. 17 1979 Bounds in the Neumann problem for second order uniformly elliptic operators. Zbl 0111.09701Bramble, J. H.; Payne, L. E. 17 1962 A Saint-Venant principle for nonlinear elasticity. Zbl 0519.73005Knops, R. J.; Payne, L. E. 16 1983 On a priori bounds in the Cauchy problem for elliptic equations. Zbl 0199.16603Payne, L. E. 16 1970 Some inequalities for vector functions with applications in elasticity. Zbl 0109.16806Bramble, J. H.; Payne, L. E. 16 1962 Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder. Zbl 0762.35012Flavin, J. N.; Knops, R. J.; Payne, L. E. 15 1992 Decay bounds for solutions of second order parabolic problems and their derivatives. Zbl 0832.35019Payne, L. E.; Philippin, G. A. 15 1995 Some Phragmén-Lindelöf type results for the biharmonic equation. Zbl 0810.31001Payne, L. E.; Schaefer, P. W. 15 1994 Energy bounds for some nonstandard problems in partial differential equations. Zbl 1121.35331Payne, L. E.; Schaefer, P. W. 15 2002 Note on a lemma of Finn and Gilbar. Zbl 0078.40002Payne, L. E.; Weinberger, H. F. 15 1957 On two free boundary problems in potential theory. Zbl 0760.31003Payne, L. E.; Philippin, G. A. 14 1991 Isoperimetric inequalities in the torsion and clamped membrane problems for convex plane domains. Zbl 0521.73056Payne, 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 0481.35022Payne, L. E. 14 1981 Some isoperimetric norm bounds for solutions of the Helmholtz equation. Zbl 0256.35023Payne, Lawrence E.; Rayner, Margaret E. 14 1973 Spatial decay bounds in the channel flow of an incompressible viscous fluid. Zbl 1185.35024Lin, Changhao; Payne, Lawrence E. 14 2004 Phragmén-Lindelöf and continuous dependence type results in generalized heat conduction. Zbl 0864.35051Payne, L. E.; Song, J. C. 13 1996 On Hopf type maximum principles for convex domains. Zbl 0367.35023Payne, L. E.; Sperb, Rene; Stakgold, Ivar 13 1977 Some general remarks on improperly posed problems for partial differential equations. Zbl 0257.35079Payne, L. E. 13 1973 Uniqueness and continuous dependence criteriafor the Navier-Stokes equations. Zbl 0259.35068Payne, L. E. 13 1972 Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Zbl 1277.35075Payne, L. E.; Philippin, G. A. 23 2013 Lower bounds for blow-up in a model of chemotaxis. Zbl 1231.35027Payne, L. E.; Song, J. C. 28 2012 Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions. Zbl 1255.35059Payne, L. E.; Philippin, G. A. 18 2012 Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Zbl 1241.35027Payne, L. E.; Philippin, G. A. 17 2012 Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II. Zbl 1198.35131Payne, L. E.; Philippin, G. A.; Piro, S. Vernier 53 2010 Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. I. Zbl 1227.35173Payne, L. E.; Philippin, G. A.; Vernier Piro, S. 42 2010 Blow-up and decay criteria for a model of chemotaxis. Zbl 1195.35058Payne, L. E.; Song, J. C. 7 2010 Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Zbl 1184.35077Payne, L. E.; Schaefer, P. W. 48 2009 Lower bounds for blow-up time in a nonlinear parabolic problem. Zbl 1177.35043Payne, L. E.; Song, J. C. 42 2009 Decay for a Keller-Segel chemotaxis model. Zbl 1180.35529Payne, L. E.; Straughan, B. 8 2009 An ill-posed problem for the heat equation. Zbl 1179.35339Payne, L. E.; Philippin, G. A. 1 2009 Blow-up phenomena for some nonlinear parabolic problems. Zbl 1159.35382Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 55 2008 Bounds for blow-up time in nonlinear parabolic problems. Zbl 1139.35055Payne, L. E.; Philippin, G. A.; Schaefer, P. W. 43 2008 Blow-up in parabolic problems under Robin boundary conditions. Zbl 1156.35408Payne, L. E.; Schaefer, P. W. 24 2008 Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. Zbl 1139.35085Lin, Changhao; Payne, L. E. 20 2008 Blow-up phenomena for some nonlinear parabolic systems. Zbl 1169.35340Payne, L. E.; Schaefer, P. W. 9 2008 Spatial decay bounds for double diffusive convection in Brinkman flow. Zbl 1133.35021Payne, L. E.; Song, J. C. 7 2008 Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. Zbl 1110.35031Payne, L. E.; Schaefer, P. W. 91 2007 Structural stability for a Brinkman fluid. Zbl 1208.35011Lin, Changhao; Payne, L. E. 25 2007 Structural stability for the Brinkman equations of flow in double diffusive convection. Zbl 1167.35435Lin, Changhao; Payne, L. E. 19 2007 Spatial decay in a double diffusive convection problem in Darcy flow. Zbl 1110.76051Payne, L. E.; Song, J. C. 11 2007 A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov. Zbl 1136.35110Payne, L. E. 11 2007 Lower bounds for the blow-up time in a temperature dependent Navier-Stokes flow. Zbl 1124.35057Payne, L. E.; Song, J. C. 11 2007 Continuous dependence on the geometry and on the initial time for a class of parabolic problems. I. Zbl 1133.35010Payne, L. E.; Philippin, G. A.; Proytcheva, V. 5 2007 Spatial decay in a cross-diffusion problem. Zbl 1134.35018Payne, L. E.; Song, J. C. 1 2007 Lower bounds for blow-up time in parabolic problems under Neumann conditions. Zbl 1110.35032Payne, L. E.; Schaefer, P. W. 80 2006 On a proposed model for heat conduction. Zbl 1126.80003Payne, L. E.; Song, J. C. 8 2006 Decay bounds for solutions of second order parabolic problems and their derivatives. IV. Zbl 1096.35065Payne, 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 1138.35037Payne, L. E.; Philippin, G. A.; Vernier-Piro, S. 6 2006 Continuous dependence inequalities for a class of quasilinear parabolic problems. Zbl 1100.35013Payne, L. E.; Philippin, G. A.; Safoui, A. 1 2006 Alternative spatial growth and decay for constrained motion in an elastic cylinder. Zbl 1074.74009Knops, R. J.; Payne, L. E. 9 2005 Some nonstandard problems in generalized heat conduction. Zbl 1080.35034Payne, L. E.; Schaefer, P. W.; Song, J. C. 9 2005 Improved spatial decay bounds in generalized heat conduction. Zbl 1082.35078Payne, L. E.; Song, J. C. 5 2005 Spatial decay bounds for a class of quasi-linear parabolic initial-boundary value problems. Zbl 1349.35173Payne, L. E.; Philippin, G. A. 2 2005 On two classes of nonstandard parabolic problems. Zbl 1083.35132Ames, K. A.; Payne, L. E.; Song, J. C. 2 2005 Energy and pointwise bounds in some non-standard parabolic problems. Zbl 1056.35104Ames, K. A.; Payne, L. E.; Schaefer, P. W. 23 2004 Some non-standard problems in viscous flow. Zbl 1174.76307Payne, L. E.; Schaefer, P. W.; Song, J. C. 17 2004 Spatial decay bounds in the channel flow of an incompressible viscous fluid. Zbl 1185.35024Lin, Changhao; Payne, Lawrence E. 14 2004 On a nonstandard problem for heat conduction in a cylinder. Zbl 1052.35066Ames, K. A.; Payne, L. E.; Schaefer, P. W. 12 2004 Spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid. Zbl 1075.35054Lin, Changhao; Payne, Lawrence E. 9 2004 Decay bounds for solutions of second order parabolic problems and their derivatives. III. Zbl 1072.35097Payne, L. E.; Philippin, G. A. 7 2004 Decay bounds for solutions of second order parabolic problems and their derivatives. II. Zbl 1069.35506Payne, L. E.; Philippin, G. A. 6 2004 Continuous dependence of heat flux on spatial geometry for the generalized Maxwell-Cattaneo system. Zbl 1054.35007Lin, Changhao; Payne, L. E. 5 2004 Improved bounds for some nonstandard problems in generalized heat conduction. Zbl 1065.35081Payne, L. E.; Schaefer, P. W.; Song, J. C. 3 2004 Spatial decay estimates for the Maxwell-Cattaneo equations with mixed boundary conditions. Zbl 1065.35134Payne, L. E.; Song, J. C. 1 2004 Temporal decay bounds in generalized heat conduction. Zbl 1058.35142Payne, L. E.; Song, J. C. 1 2004 Energy bounds for some nonstandard problems in partial differential equations. Zbl 1121.35331Payne, L. E.; Schaefer, P. W. 15 2002 Spatial decay bounds for the Forchheimer equations. Zbl 1211.76119Payne, L. E.; Song, J. C. 7 2002 Growth and decay in generalized thermoelasticity. Zbl 1211.74076Payne, L. E.; Song, J. C. 2 2002 Decay bounds in initial-boundary value problems for nonlinear parabolic systems. Zbl 1011.35072Payne, L. E.; Schaefer, P. W. 2 2002 Effect of anisotropic permeability on Darcy’s law. Zbl 0984.76024Payne, L. E.; Rodrigues, J. F.; Straughan, B. 33 2001 Spatial decay in the pipe flow of a viscous fluid interfacing a porous medium. Zbl 1034.35103Ames, K. A.; Payne, L. E.; Song, J. C. 7 2001 Continuous dependence on spatial geometry for the generalized Maxwell-Cattaneo system. Zbl 0994.35024Lin, Changhao; Payne, L. E. 3 2001 Eigenvalue and eigenfunction inequalities for the elastically supported membrane. Zbl 0986.35081Payne, L. E.; Schaefer, P. W. 2 2001 Continuous dependence on base data in an elastic prismatic cylinder. Zbl 1034.74007Knops, R. J.; Payne, L. E. 1 2001 Convergence results for generalized heat condution as the relaxation time tends to zero. Zbl 0977.35015Payne, L. E.; Song, J. C. 1 2001 Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Zbl 1136.35318Payne, L. E.; Straughan, B. 19 2000 Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows. Zbl 0970.76097Payne, L. E.; Song, J. C. 17 2000 A naturally efficient numerical technique for porous convection stability with non-trivial boundary conditions. Zbl 0977.76070Payne, 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 0963.35091Payne, L. E.; Philippin, G. A. 4 2000 Convergence and continuous dependence for the Brinkman-Forchheimer equations. Zbl 1136.76448Payne, L. E.; Straughan, B. 70 1999 Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Zbl 0933.76091Payne, L. E.; Song, J. C.; Straughan, B. 55 1999 Continuous dependence on modeling for some well-posed perturbations of the backward heat equation. Zbl 0928.35015Ames, K. A.; Payne, L. E. 17 1999 Convergence of the equations for a Maxwell fluid. Zbl 1136.76310Payne, L. E.; Straughan, B. 11 1999 Effect of errors in the spatial geometry for temperature dependent Stokes flow. Zbl 0935.76020Payne, L. E.; Straughan, B. 10 1999 Growth and decay results in heat conduction problems with nonlinear boundary conditions. Zbl 0919.35066Payne, 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 0906.35067Payne, L. E.; Straughan, B. 64 1998 Structural stability for the Darcy equations of flow in porous media. Zbl 0912.76088Payne, L. E.; Straughan, B. 36 1998 Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Zbl 0982.35119Ames, K. A.; Payne, L. E. 27 1998 Bounds and decay results for some second-order semilinear elliptic problems. Zbl 0917.35036Payne, 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 0893.76090Payne, L. E.; Song, J. C. 22 1997 Continuous dependence on the initial-time geometry in generalized heat conduction. Zbl 0871.35013Payne, L. E.; Song, J. C. 8 1997 Continuous dependence results for a problem in penetrative convection. Zbl 0892.35079Ames, Karen A.; Payne, Lawrence E. 8 1997 Saint-Venant’s principle in linear isotropic elasticity for incompressible or nearly incompressible materials. Zbl 0907.73010Horgan, C. O.; Payne, L. E. 7 1997 Continuous dependence on initial-time and spatial geometry in generalized heat conduction. Zbl 0889.35011Payne, L. E.; Song, J. C. 3 1997 Continuous dependence results for an ill-posed problem in nonlinear viscoelasticity. Zbl 0906.73030Ames, Karen A.; Payne, Lawrence E. 1 1997 Spatial decay estimates for a coupled system of second-order quasilinear partial differential equations arising in thermoelastic finite anti-plane shear. Zbl 0887.35051Horgan, 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 0848.76089Payne, L. E.; Straughan, B. 32 1996 Phragmén-Lindelöf and continuous dependence type results in generalized heat conduction. Zbl 0864.35051Payne, 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 0890.73014Knops, 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 1001.74524Horgan, C. O.; Payne, L. E. 2 1996 A special class of maximum principles with applications to nonlinear boundary value problems. Zbl 0845.35013Payne, L. E. 1 1996 Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region. Zbl 0884.35041Knops, R. J.; Payne, L. E. 1 1996 Decay bounds for solutions of second order parabolic problems and their derivatives. Zbl 0832.35019Payne, L. E.; Philippin, G. A. 15 1995 Continuous dependence on initial-time geometry for a thermoelastic system with sign-indefinite elasticities. Zbl 0857.35128Ames, K. A.; Payne, L. E. 10 1995 A Phragmen-Lindelöf alternative for a class of quasilinear second order parabolic problems. Zbl 0833.35018Lin, Changhao; Payne, L. E. 8 1995 Pointwise bounds and spatial decay estimates in heat conduction problems. Zbl 0849.35011Payne, L. E.; Philippin, G. A. 7 1995 On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Zbl 0819.76077Ames, K. A.; Payne, L. E. 20 1994 Some Phragmén-Lindelöf type results for the biharmonic equation. Zbl 0810.31001Payne, L. E.; Schaefer, P. W. 15 1994 On overdetermined boundary value problems for the biharmonic operator. Zbl 0810.35020Payne, L. E.; Schaefer, P. W. 10 1994 Phragmen-Lindelöf type results for second order quasilinear parabolic equations in \(\mathbb{R}^ 2\). Zbl 0799.35124Lin, Changhao; Payne, Lawrence E. 9 1994 The influence of domain and diffusivity perturbations on the decay of end effects in heat conduction. Zbl 0809.35034Lin, Changhao; Payne, L. E. 8 1994 Continuous dependence results for solutions of the Navier-Stokes equations backward in time. Zbl 0814.35144Ames, K. A.; Payne, L. E. 8 1994 Uniqueness and continuous dependence of solutions to a multidimensional thermoelastic contact problem. Zbl 0809.73055Ames, K. A.; Payne, L. E. 7 1994 On gradient maximum principles for quasilinear elliptic equations. Zbl 0820.35018Payne, L. E.; Philippin, G. A. 4 1994 Stabilizing the backward heat equation against errors in the initial time geometry. Zbl 0900.35042Ames, K. A.; Payne, L. E. 2 1994 A Phragmén-Lindelöf principle for the equation of a surface of constant mean curvature. Zbl 0792.35066Knops, R. J.; Payne, L. E. 1 1994 Spatial decay estimates in time-dependent Stokes flow. Zbl 0787.35060Ames, K. A.; Payne, L. E.; Schaefer, P. W. 18 1993 Phragmén-Lindelöf type results for harmonic functions with nonlinear boundary conditions. Zbl 0790.31002Horgan, C. O.; Payne, L. E. 17 1993 On the asymptotic behavior of solutions of linear second-order boundary- value problems on a semi-infinite strip. Zbl 0819.35014Horgan, C. O.; Payne, L. E. 10 1993 ...and 161 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,672 Authors 118 Payne, Lawrence Edward 85 Quintanilla de Latorre, Ramón 66 Straughan, Brian 37 Philippin, Gérard A. 36 Knops, Robin J. 33 Zhou, Jun 31 Schaefer, Philip W. 30 Saanouni, Tarek 28 Xu, Runzhang 27 Ding, Juntang 25 Repin, Sergeĭ Igorevich 24 Levine, Howard Allen 23 Liu, Yan 23 Song, Jong Chul 19 Fang, Zhongbo 19 Horgan, Cornelius Oliver 19 Lin, Changhao 19 Sperb, Rene P. 19 Vernier-Piro, Stella 19 Vohralík, Martin 19 Zhang, Jian 18 Cheng, Qingming 18 Chiriţă, Stan 18 Xia, Changyu 17 Ames, Karen A. 17 Enache, Cristian 17 Wang, Qiaoling 16 Nguyen Huy Tuan 16 Ye, Yaojun 15 Ashbaugh, Mark S. 15 Bandle, Catherine 14 Ciarletta, Michele 14 Marin, Marin I. 13 Benguria, Rafael D. 13 Li, Yuanfei 13 Marras, Monica 13 Rammaha, Mohammad A. 13 Ukhlov, Alexander Dadar-Oolovich 12 Gazzola, Filippo 12 Han, Yuzhu 12 Hersch, Joseph 12 Kalantarov, Varga K. 12 Leseduarte, Mari Carme 12 Viglialoro, Giuseppe 11 Bloom, Frederick 11 Chen, Hua 11 Esquivel-Avila, Jorge Alfredo 11 Gol’dshtein, Vladimir Mikhailovich 11 Rionero, Salvatore 10 Dökmeci, M. Cengiz 10 Miranville, Alain M. 10 Shang, Yadong 10 Song, Xianfa 10 Steinerberger, Stefan 10 Sun, Hejun 10 Trombetti, Cristina 10 Xu, Guangyu 10 Yamamoto, Masahiro 9 Carstensen, Carsten 9 Ding, Hang 9 Fu, Chuli 9 Hill, Antony A. 9 Ibragimov, Akif 9 Liu, Wenjun 9 Mu, Chunlai 9 Nakanishi, Kenji 9 Nitsch, Carlo 9 Trong, Dang Duc 9 Valdinoci, Enrico 8 Chen, Daguang 8 Galdi, Giovanni Paolo 8 Gan, Zaihui 8 Gavitone, Nunzia 8 Grossi, Massimo 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 Yang, Hongcang 8 Yang, Yanbing 8 Zeng, Lingzhong 7 Aulisa, Eugenio 7 Bucur, Dorin 7 Carasso, Alfred S. 7 Della Pietra, Francesco 7 Di, Huafei 7 Hoang, Luan Thach 7 Hon, Yiu-Chung 7 Kawohl, Bernd 7 Le Xuan Truong 7 Li, Fengjie 7 Liang, Fei 7 Liu, Genqian 7 Liu, Yang 7 Matevosyan, Hovik A. ...and 2,572 more Authors all top 5 Cited in 392 Serials 196 Journal of Mathematical Analysis and Applications 142 ZAMP. 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Serie IV 8 Calcolo 8 Mathematika 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Communications in Contemporary Mathematics 8 Journal of Spectral Theory 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Potential Analysis 7 SIAM Journal on Scientific Computing 7 Electronic Journal of Differential Equations (EJDE) 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 7 Open Mathematics 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 Results in Mathematics ...and 292 more Serials all top 5 Cited in 51 Fields 2,082 Partial differential equations (35-XX) 514 Mechanics of deformable solids (74-XX) 432 Fluid mechanics (76-XX) 350 Numerical analysis (65-XX) 161 Global analysis, analysis on manifolds (58-XX) 108 Operator theory (47-XX) 107 Differential geometry (53-XX) 105 Calculus of variations and optimal control; optimization (49-XX) 103 Classical thermodynamics, heat transfer (80-XX) 80 Potential theory (31-XX) 68 Biology and other natural sciences (92-XX) 65 Functional analysis (46-XX) 64 Ordinary differential equations (34-XX) 55 Real functions (26-XX) 36 Probability theory and stochastic processes (60-XX) 35 Quantum theory (81-XX) 33 Functions of a complex variable (30-XX) 32 Convex and discrete geometry (52-XX) 29 Integral equations (45-XX) 26 Optics, electromagnetic theory (78-XX) 26 Statistical mechanics, structure of matter (82-XX) 23 Dynamical systems and ergodic theory (37-XX) 17 Systems theory; control (93-XX) 16 Measure and integration (28-XX) 13 Special functions (33-XX) 11 Geophysics (86-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Statistics (62-XX) 10 Mechanics of particles and systems (70-XX) 9 Combinatorics (05-XX) 9 Approximations and expansions (41-XX) 9 Operations research, mathematical programming (90-XX) 9 Information and communication theory, circuits (94-XX) 6 Integral transforms, operational calculus (44-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 Computer science (68-XX) 4 Relativity and gravitational theory (83-XX) 3 Difference and functional equations (39-XX) 2 Number theory (11-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 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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