具抛物型动力边界条件的Laplace方程解的爆破

Blow-up for Laplace Equation with Dynamical Boundary Conditions of Parabolic Type

摘要: 讨论了具非线性动力边界条件的Laplace方程解的爆破,在边界条件为半线性抛物型且初始能量为负及边界源项满足一定条件下,利用凸性方法得到了解的爆破性.

Abstract: The blow-up for Laplace equation with dynamical boundary condition is considered . By the concavity method, the blow-up of the solution is proved under the condition that the boundary condition is semilinear parabolic type and the initial energy is negative.