On the Decay of Almost Periodic Solutions of Anisotropic Degenerate Parabolic-Hyperbolic Equations

TL;DR

This paper investigates the existence, uniqueness, and decay properties of almost periodic solutions to a class of nonlinear anisotropic degenerate hyperbolic-parabolic equations, establishing well-posedness and initial trace results.

Contribution

It introduces a new framework for weak entropy solutions with minimal initial data assumptions and proves decay and trace properties for these solutions.

Findings

Well-posedness of solutions under weak initial data assumptions

Decay estimates for solutions over time

Existence of strong traces at initial time

Abstract

We discuss the well-posedness and decay of Besicovitch almost periodic solutions for a class of nonlinear degenerate anisotropic hyperbolic-parabolic equations. In our definition of weak entropy solution the initial data is only assumed in a weak sense, and in this connection the strong trace of the solution in the initial time hyperplane is also established.