Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system

Title:

Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system

Creator:

Chen, Yujuan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6e21c4f0-13d5-495a-a50d-6f93b0a9c6e7
uuid:6e21c4f0-13d5-495a-a50d-6f93b0a9c6e7

Subject:

strongly coupled, degenerate parabolic system, nonlocal source, global existence, and blow-up

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form $$ u_t = v^p\biggl (\Delta u + a\int _\Omega u \,{\rm d} x\biggr ),\quad v_t =u^q\biggl (\Delta v + b\int _\Omega v \,{\rm d} x\biggr ) $$ with null Dirichlet boundary conditions. By using the standard approximation method, we first give a series of fine a priori estimates for the solution of the corresponding approximate problem. Then using the diagonal method, we get the local existence and the bounds of the solution $(u,v)$ to this problem. Moreover, a necessary and sufficient condition for the non-global existence of the solution is obtained. Under some further conditions on the initial data, we get criteria for the finite time blow-up of the solution.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

675-688

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:3

Harvested from:

CDK

Metadata only:

false