一类热方程边值问题解的存在唯一性

Existence and Uniqueness of Solutions for a Class of Boundary Value Problems of Thermal Equations

研究一类热方程具狄利克雷边界条件的第一边值问题.利用Poincaré不等式导出弱解的极值原理,并运用逼近理论和Arzela-Ascoli定理证得了其边值问题解的存在唯一性.

The first boundary value problem for a class of heat equation with dirichlet boundary conditions was dealed.The extremum principle of the weak solution was derived by using Poincare inequality,and the existence and uniqueness of the solution with the boundary value problem was proved by using the approximation theory and arzela-ascoli theorem.