Existence and uniqueness of solutions to a class of singular diffusion problems

Abstract

Existence, uniqueness, and non-uniqueness results are given for a class of singular diffusion problems with variable diffusion rates. Continuity arguments are used on related initial value problems to produce the existence results. Uniqueness criteria are established for different sets of hypotheses and non-uniqueness results are discussed when these hypotheses fail.

Keywords:

• Singular diffusion problem
• existence
• uniqueness

AMS(MOS)::

• 35K10