Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations 论文

摘要

CONTENTS Introduction Chapter I. Existence and uniqueness of generalized solutions of the Cauchy problem and of initial boundary-value problems § 1.1. Theorems of existence and non-existence § 1.2. Uniqueness theorems Chapter II. Estimates and differential properties of generalized solutions § 2.1. The character of the dependence on the data § 2.2. Regularity and non-regularity Chapter III. Behaviour of generalized solutions for small values of time § 3.1. Finite rate of propagation of perturbations § 3.2. Inertia § 3.3. Shrinking of the size of the support Chapter IV. Behaviour of generalized solutions for large values of time § 4.1. Stabilization in finite time § 4.2. Localization of perturbations § 4.3. Asymptotic formulae References