Boundary-value problems with non-local condition for degenerate parabolic equations

TL;DR

This paper investigates boundary-value problems for degenerate parabolic equations with three lines of degeneration, establishing uniqueness conditions and demonstrating nontrivial solutions when these conditions are not met.

Contribution

It introduces the 'a-b-c' method to prove uniqueness theorems and explores solutions beyond the uniqueness conditions for degenerate parabolic equations.

Findings

Proved uniqueness theorems using the 'a-b-c' method.

Identified nontrivial solutions when parameter conditions are violated.

Analyzed equations with three lines of degeneration.

Abstract

In this work we deal with degenerate parabolic equations with three lines of degeneration. Using "a-b-c" method we prove the uniqueness theorems defining conditions to parameters. We show nontrivial solutions for considered problems, when uniqueness conditions to parameters, participating in the equations are not fulfilled.