Blow-up solutions for reaction diffusion equations with nonlocal boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Ding, Juntang¹  Kou, Wei¹ 

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

关键词: Reaction diffusion equation;    Blow-up;    Nonlocal boundary condition;    Lower bound;   

DOI  :  10.1016/j.jmaa.2018.09.021

来源: Elsevier

【 摘 要 】

We devote to investigating the following nonlinear reaction diffusion equations with nonlocal boundary conditions {u(t) = del . (rho(u)del u) _ k(1)(t) f(u) in D x (0, t*), partial derivative u/partial derivative v = k(2) (t) integral(D) g(u)dx on partial derivative D x(0,t*), u(x, 0 = u(0)(x) >= 0 in <(Dover bar>, where D is a bounded convex region in R-n (n >= 2), and the boundary partial derivative D is smooth. By constructing some auxiliary functions and using differential inequality technique, we derive that the solution blows up at some finite time. Moreover, upper and lower bounds of the blow-up time are obtained. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free