拟线性退化抛物型方程组解的整体存在性和爆破

Abstract

Abstract:

This paper investigates the nonnegative solutions of quasi-linear degenerate
parabolic system

u_t-div(|▽u|^p-2 ▽u) =av^α, v_t-div(|▽v|^q-2 ▽v) =bu^β
with zero Dirichlet boundary conditions in a smooth bounded domain Ω( R^N(N≥ 1), where p, q>2, α, β ≥ 1, a, b>0 are constants. It is obtained that whether the solution blows up in finite time or not depends on the initial data, the coefficients a and b, and the relation between αβ and (p-1)(q-1).

Key words: Quasi-linear degenerate parabolic system, Nonlinear source, Global
existence, Blow-up

CLC Number:

35K65

Li Fucai. Global Existence and Blow-up of Solutions to a Quasi-linear Degenerate Parabolic System[J].Acta mathematica scientia,Series A, 2008, 28(6): 1187-1193.

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Global Existence and Blow-up of Solutions to a Quasi-linear Degenerate Parabolic System

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