摘要
This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.
研究了一个具有齐次Dirichlet边界条件以及正的初值条件的退化抛物型方程组 :ut=Δum +vplnα(h +u) ,vt=Δvn+uqlnβ(h +v) .该方程组描述了一个具有 2种连续介质的燃烧过程及热扩散过程 .本文利用上。
