Global nonexistence for the Cauchy problem of some nonlinear reaction-diffusion systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:268

Article

Kirane, M ; Qafsaoui, M

关键词: fractal diffusion operator;    nonlinear reaction-diffusion systems;    strongly coupled systems;    degenerate systems;    porous media;    blow-up;   

DOI  :  10.1006/jmaa.2001.7819

来源: Elsevier

【 摘 要 】

We, first, consider the parabolic equation u(t) = -(-Delta)(alpha/2)u(m) + a(x).delu(q) + f(t,x)\u\(cp) + s(t,x), t > 0, x is an element of R-N, where (-Delta)(alpha/2) is the alpha/2-fractional power of the Laplacian -Delta which for 0 < alpha less than or equal to 2 stands for impurities and f(t, x) and w(t, x) are given nonnegative functions, and find its critical exponent. Then, we consider the criticality for five systems of strongly coupled parabolic equations, two of them with nonlinear convective terms. Our results answer positively some open problems raised recently by Bandle, Deng, Levine, and Zhang. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free