脉冲抛物型方程柯西问题解的存在性与爆破性质

Existence and Blow-up for the Cauchy Problem of Impulsive Parabolic Equation

考虑了含有脉冲的半线性反应扩散方程的柯西问题 ,利用上下解原理证明了其解的存在性与唯一性 ,并建立比较原理 ,由此得出结论 :当反应项满足一定条件时 ,解会在有限时刻发生爆破 .

An Cauchy problem of impulsive semilinear reactive diffusive equation is considered. The existence and uniqueuess are proved by using upper and lower solutions. Moreover, using comparing theorem we get the solution will blow up at a finite time when the reactive function suits to some condition.