非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程解的爆破现象

Blow-up Phenomena of Solutions to a Nonlocal Porous Medium Parabolic Equation with Space-dependent Coefficients and Inner Absorption Terms Under Nonlinear Boundary Conditions

本文研究了非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程解的爆破问题.运用微分不等式技巧,得到了高维空间上非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程全局解的条件.同时,通过构造能量表达式,应用Sobolev不等式等技巧,推出了爆破发生时解的爆破时间上界和下界估计.

In this paper,we study blow-up phenomena of solutions to a nonlocal porous medium parabolic equation with space-dependent coeficients and inner absorp-tion terms under nonlinear boundary conditions.By using a differential technique,we obtain the suficient conditions for the global existence for the parabolic equation with space-dependent coefficients and inner absorption terms under nonlinear boundary conditions in high dimensional spaces.Moreover,an upper bound and a lower bound estimates of blow up time are derived by formulating energy expressions and using Sobolev inequalities and other differential methods.