Bounds for blow-up time for the heat equation under nonlinear boundary conditions

L. E. Payne; P. W. Schaefer

doi:10.1017/S0308210508000802

Abstract

A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Payne, L.E. Philippin, G.A. and Vernier Piro, S. 2010. Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, II. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, Issue. 4, p. 971.

Payne, L. E. Philippin, G. A. and Vernier Piro, S. 2010. Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I. Zeitschrift für angewandte Mathematik und Physik, Vol. 61, Issue. 6, p. 999.

ENACHE, CRISTIAN 2011. LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS. Glasgow Mathematical Journal, Vol. 53, Issue. 3, p. 569.

Enache, Cristian 2011. Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition. Applied Mathematics Letters, Vol. 24, Issue. 3, p. 288.

Payne, Lawrence E. and Philippin, Gérard A. 2012. Blow-Up Phenomena for a Class of Parabolic Systems with Time Dependent Coefficients. Applied Mathematics, Vol. 03, Issue. 04, p. 325.

Deng, Keng and Dong, Zhihua 2012. Blow-up for the heat equation with a general memory boundary condition. Communications on Pure and Applied Analysis, Vol. 11, Issue. 5, p. 2147.

Li, Fushan and Li, Jinling 2012. Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions. Journal of Mathematical Analysis and Applications, Vol. 385, Issue. 2, p. 1005.

Liu, Yan 2013. Lower bounds for the blow-up time in a non-local reaction diffusion problem under nonlinear boundary conditions. Mathematical and Computer Modelling, Vol. 57, Issue. 3-4, p. 926.

Payne, L. and Philippin, G. 2013. Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Proceedings of the American Mathematical Society, Vol. 141, Issue. 7, p. 2309.

Liu, Yan Luo, Shiguang and Ye, Yunhua 2013. Blow-up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions. Computers & Mathematics with Applications, Vol. 65, Issue. 8, p. 1194.

Liu, Yan 2013. Blow-up phenomena for the nonlinear nonlocal porous medium equation under Robin boundary condition. Computers & Mathematics with Applications, Vol. 66, Issue. 10, p. 2092.

Bao, Aiguo and Song, Xianfa 2014. Bounds for the blowup time of the solutions to quasi-linear parabolic problems. Zeitschrift für angewandte Mathematik und Physik, Vol. 65, Issue. 1, p. 115.

Tang, Gusheng Li, Yuanfei and Yang, Xitao 2014. Lower bounds for the blow-up time of the nonlinear non-local reaction diffusion problems in R N ( N ≥ 3 ). Boundary Value Problems, Vol. 2014, Issue. 1,

Li, Fushan and Li, Jinling 2014. Global existence and blow-up phenomena for p-Laplacian heat equation with inhomogeneous Neumann boundary conditions. Boundary Value Problems, Vol. 2014, Issue. 1,

Lv, Xiaoshuang and Song, Xianfa 2014. Bounds of the blowup time in parabolic equations with weighted source under nonhomogeneous Neumann boundary condition. Mathematical Methods in the Applied Sciences, Vol. 37, Issue. 7, p. 1019.

Li, Jin 2014. Blow-up in the Parabolic Problems under Nonlinear Boundary Conditions. Journal of Networks, Vol. 9, Issue. 3,

Song, Xianfa and Lv, Xiaoshuang 2014. Bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source. Applied Mathematics and Computation, Vol. 236, Issue. , p. 78.

Zhou, Jun 2015. Lower bounds for blow-up time of two nonlinear wave equations. Applied Mathematics Letters, Vol. 45, Issue. , p. 64.

Luo, Peng 2015. Blow‐up phenomena for a pseudo‐parabolic equation. Mathematical Methods in the Applied Sciences, Vol. 38, Issue. 12, p. 2636.

Wang, Ning Song, Xianfa and Lv, Xiaoshuang 2016. Estimates for the blowup time of a combustion model with nonlocal heat sources. Journal of Mathematical Analysis and Applications, Vol. 436, Issue. 2, p. 1180.

Download full list

Article contents

Bounds for blow-up time for the heat equation under nonlinear boundary conditions

Abstract

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Bounds for blow-up time for the heat equation under nonlinear boundary conditions

Abstract

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests