反应-对流-扩散方程组的齐次Dirichlet外区域问题的Fujita型定理

利用能量比较方法和比较原理考虑含源和对流项的耦合非线性扩散方程组的齐次Dirichlet外区域问题解的整体存在和爆破性质,确定了临界Fujita曲线,并建立了Fujita型爆破定理.结果表明,该临界Fujita曲线依赖于方程组的空间维数、对流项和反应项.

Fujita Type Theorem for Homogeneous Dirichlet Problems inExterior Domain of Reaction Convection Diffusion Systems

Using the energy comparison method and comparison principle, we considered the global existence and blow up properties of the homogeneous Dirichlet problems in exterior domain of coupled nonlinear diffusion systems with reactions and convections, determined the critical Fujita curve and established the Fujita type blow up theorem. The results show that the critical Fujita curve depends on the spacial dimension, convection and reaction terms of the systems.