两个空间变量的拟线性抛物方程初值问题解的正则性

Regularity of Generalized Solutions of Cauchy Problem for Quasilinear Parabolic Equations with Two-Dimensional Space

本文研究了两个空间变量的拟线性退缩抛物方程Cauchy问题广义解的正则性问题.推广了文献[1]的结果.

This paper deals with Cauchy problem for quasilinear degenerate parabolic equations with two-dimensional space of the type u_t= △(u^(1+δ)+b_i(u)-x_i,(x,t) ∈ R_t,(1) u(x,0)=u_0(x), x ∈R^2.(2) At first, the necessary estimates for the solutions of regularized problems are made.Then the regularity of generalized solutions is proved. And the existence of generalized solutions is studied.