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

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.