非线性边界条件下一致抛物型方程解的爆破

Blow-up of Solution of Uniformly Parabolic Equations with Nonlinear Boundary Conditions

为了发展一致抛物型方程解的整体存在和爆破理论,文章研究了一个非线性抛物型方程在非线性边界条件下解的爆破,以非线性抛物型方程解的泛涵的极大值原理为主要工具,结合比较原理、上下解方法和微分、积分不等式技巧,证明了其解在有限时间内具有爆破性质。

To develop the global existence and blasting theory of the solution of nonlinear parabolic equation,the paper researched a blow-up of solution of nonlinear parabolic equation with nonlinear boundary condition.It proved its solution has blow-up at finite time using the maximum principle of nonlinear singular parabolic,together with comparative principle,the upper and lower solutions methods and differential calculus and integral inequalities skills.