具梯度耗散与非局部源牛顿渗流方程解的爆破性质

Blow-up Properties of Solutions to Newtonian Filtration Equation with Dissipative Gradient and Nonlocal Source

利用能量估计方法考虑一类具有梯度耗散项和非局部源项的牛顿渗流方程的初边值问题解的爆破现象,给出解是否发生爆破的条件,并借助适当的辅助函数和Sobolev不等式对解发生爆破的时间上下界进行估计.

We considered blow-up phenomena of solutions to the initial boundary value problem for a class of Newtonian filtration equations with dissipative gradient and nonlocal source terms by energy estimation method.We gave the condition whether the blow-up of solution occurred or not.Then by using the suitable auxiliary function and Sobolev inequalities,we estimated the upper and lower bounds of blow-up time of solutions.