一类半线性抛物边值问题的最大值原理

Maximum Principles for a Class of Semilinear Parabolic Boundary-Value Problems

文中构造了一类具有 Dirichlet或 Neumann边界条件的半线性抛物方程 u,t=Δu+ f( x,u,q,t) ( q=| u| 2 )的解的一个辅助函数 ,对其使用 Hopf最大值原理和黎曼几何理论 ,从而获得了该函数的最大值原理 ,据此原理获得了梯度 q和解

By constructing an auxiliary function defined on solutions of the semilinear parabolic equations \$u,\-t= Δ u+f(x,u,q,t) (q=|u|\+2),\$ subject to nonnegative initial date and either Dirichlet or Neumann boundary conditions, and using Hopf's maximum principles and Riemannian geometry theorm on it, the maximum principles of this function are obtained. The estimation of gradient q and the estimation of the solution u are given.