QUASI-LINEAR SECOND-ORDER PARABOLIC EQUATIONS WITH MANY INDEPENDENT VARIABLES

Abstract

CONTENTS § 1. Introduction § 2. A priori estimates for the solutions of linear parabolic equations § 3. A priori estimates for the solutions of quasi-linear parabolic equations § 4. Existence theorems for solutions of the first boundary value problem and Cauchy's problem in the large for quasi-linear parabolic equations § 5. An approximate solution of the boundary value problem and Cauchy's problem for quasi-linear parabolic equations. Generalized solutions of these problems § 6. Theorems on a priori estimates and the solvability of the Dirichlet problem for quasi-linear elliptic equations with many independent variables References