关键词: 拟线性退化抛物型方程组, 非线性源, 整体存在, 爆破

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