Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions-Reference-Cited by-同舟云学术

Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions

Published:2020-06-05 Issue: Volume:2020 Page:1-7
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Ouyang Baiping¹,Fan Wei²,Lin Yiwu³^ORCID

Affiliation:

1. College of Data Science, Huashang College Guangdong University of Finance & Economics, Guangzhou 511300, China

2. The School of Gifted Young, University of Science and Technology of China, Hefei, China

3. Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China

Abstract

In this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions. Using the technique of a first-order differential inequality and the Sobolev inequalities, we can get the energy expression which satisfies the differential inequality. The lower bound for the blow-up time could be obtained if blow-up does really occur in high dimensions.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modelling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2020/7480676.pdf

Reference22 articles.

1. Global existence and finite time blow up for a degenerate reaction–diffusion system

2. Lower bounds for blow-up time in parabolic problems under Dirichlet conditions

3. Blow-up and global solutions for a class of nonlinear reaction diffusion equations under Dirichlet boundary conditions

4. Lower bounds for blow-up time in parabolic problems under Neumann conditions