拟线性抛物型方程在第三边值条件下的极大值原理

The Maximum Principle of Quasilinear Parabolic Equation on Condition of the Third Boundary Value

文章以线性抛物型方程的弱极值原理和强极值原理为主要工具,讨论了拟线性抛物型方程β(tu)=Δu+(fx,t,u)解的泛函V(x,)t=g(u)ut+h(u)和β(tu)=Δu+(fu)解的含梯度泛函P(x,t,u,u)k=塄u2+2Z()tF(u)(F'=)f,在第三边值条件下的极大值原理。

This paper discussed the maximum principle of the functional V（x,t）=g（u）ut＋h（u）of the solution βt（u）=Δu＋f（x,t,u）and the gradient functional P（x,t,u,uk）=︱▽u︱2＋2Z（t）F（u）（F＇=f） of the solutionβt（u）=Δu＋f（u）of the quasilinear parabolic equations on conditions of the third boundary value by using the weak extreme principle and strong maximum principle of linear parabolic equations.