Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions-Reference-Cited by-同舟云学术

Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions

Published:2023 Issue:5 Volume:8 Page:11822-11836
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Gou Zhanwei¹,Shi Jincheng²

Affiliation:

1. Basic Teaching Department, Guangdong Communication Polytechnic, Guangzhou 510650, China

2. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China

Abstract

<abstract><p>In this paper, we consider an initial-boundary value parabolic problem under nonlinear Neumann boundary conditions. By virtue of the modified differential inequality, lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. An upper bound for the blow-up time are specified under appropriate assumptions on the functions $ a, b, f, g, h $ and $ u_0 $.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference22 articles.

1. B. Straughan, Explosive instabilities in mechanics, Berlin: Springer, 1998. https://doi.org/10.1007/978-3-642-58807-5

2. P. Quittner, P. Souplet, Superlinear parabolic problems: Blow-up, global existence and steady states, Berlin: Birkhäuser Verlag AG, 2007.

3. C. Bandle, H. Brunner, Blow-up in diffusion equations, J. Comput. Appl. Math., 97 (1998), 3–22. https://doi.org/10.1016/S0377-0427(98)00100-9

4. J. L. Vazquez, The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation, Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, 15 (2004), 281–300.

5. F. B. Weissler, Local existence and nonexistence for semilinear parabolic equations in $L^p$, Indiana Univ. Math. J., 29 (1980), 79–102. https://doi.org/10.1512/iumj.1980.29.29007