Asymptotic Decay of Besicovitch Almost Periodic Entropy Solutions to Anisotropic Degenerate Parabolic-Hyperbolic Equations

TL;DR

This paper establishes the well-posedness and demonstrates the asymptotic decay to the mean value of Besicovitch almost periodic entropy solutions for nonlinear anisotropic degenerate parabolic-hyperbolic equations, extending decay results to a broader class of solutions.

Contribution

It introduces a novel approach to prove decay of Besicovitch almost periodic solutions, adapting techniques from periodic cases to this more general setting.

Findings

Proves well-posedness of solutions.

Shows decay to the mean value over time.

Extends decay results to Besicovitch almost periodic solutions.

Abstract

We prove the well-posedness and the asymptotic decay to the mean value of Besicovitch almost periodic entropy solutions to nonlinear aniso\-tropic degenerate parabolic-hyperbolic equations. After setting up the problem and its kinetic formulation on the Bohr compact, the main result, that is, the decay property, ia achieved by devising a suitable adaptation of the technique introduced by Chen and Perthame (2009) in their proof of the decay of periodic entropy solutions to the same equations.