NONEXISTENCE OF GLOBAL SOLUTIONS FOR A NONLINEAR PARABOLIC EQUATION WITH A FORCING TERM

被引：5

作者：

Alshehri, Aisha ^{[1
,2
]}

Aljaber, Noha ^{[1
,2
]}

Altamimi, Haya ^{[1
,2
]}

Alessa, Rasha ^{[1
,2
]}

Majdoub, Mohamed ^{[1
,2
]}

机构：

[1] Imam Abdulrahman Bin Faisal Univ, Coll Sci, Dept Math, POB 1982, Dammam, Saudi Arabia

[2] Imam Abdulrahman Bin Faisal Univ, Basic & Appl Sci Res Ctr, POB 1982, Dammam 31441, Saudi Arabia

来源：

OPUSCULA MATHEMATICA | 2023年 / 43卷 / 06期

关键词：

nonlinear heat equation; forcing term; blow-up; test-function; differential inequalities; INHOMOGENEOUS EVOLUTION-EQUATIONS; REACTION-DIFFUSION EQUATIONS; BLOW-UP; CRITICAL EXPONENTS;

D O I：

10.7494/OpMath.2023.43.6.741

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this work is to analyze the blow-up of solutions of a nonlinear parabolic equation with a forcing term depending on both time and space variables u(t) - Delta u = |x|(alpha) |u|(p) + a(t) w(x) for (t, x) is an element of (0, infinity) x R-N, where alpha is an element of R, p > 1, and a(t) as well as w(x) are suitable given functions. We generalize and somehow improve earlier existing works by considering a wide class of forcing terms that includes the most common investigated example t(sigma) w(x) as a particular case. Using the test function method and some differential inequalities, we obtain sufficient criteria for the nonexistence of global weak solutions. This criterion mainly depends on the value of the limit lim(t ->infinity) 1/t integral(t)(0) a(s) ds. The main novelty lies in our treatment of the nonstandard condition on the forcing term.

引用

页码：741 / 758

页数：18

共 34 条

[1] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].