具有非局部反应项的退化抛物方程解的爆破

Blow-up for a Degenerate Parabolic Equation with a Nonlocal Source

讨论了具有非局部反应项的退化抛物方程xαut-uxx=λeβu(x,t)0,(x,t)∈Ω×(0,T)的初边值问题解的爆破性.通过引入特征函数,通过特征值问题的性质构造出爆破因子,并利用比较原理,得出了解在有限时刻爆破.

This paper investigates the blow-up for a Dirichlet problem of a class of degenerate parabolic equation with a non-local source.xαut-uxx=λeβu（x,t）0,（x,t）∈Ω×（0,T）,By introducing the eigen-function,and through the property of eigen-value problem,the blowing-up factor is constructed,and using the comparative principle,the solution blow-up in finite time is obtained.