半线性拋物型方程的解及其梯度的最大模估计

The Estimates of Maximum Modulus of Solutions and their Gradients for a Class of Semilinar Parabolic Equations

通过建立适当的辅助函数,利用抛物型方程的极值原理,得到了半线性抛物型方程:u_1-u_(xx)=u^p(0<p<1),u_1-u_(xx)=-u^p(p=2,4,…2n,…)第一初边值问题的解及其梯度的最大模估计。

By seting up some assistant Functions suitable,the paper obtains the esti- mates of maximum modulus of solutions and their gradients for the first initial-boundary value problems of semilinaer parabolic equations: u_1-u_(xx)=u^p(0<p<1),u_1-u_(xx)=-u^p(p=2,4,6,…2n,…), with the maximum principles of parabolic equation.