Some qualitative properties of solutions of the system governing acoustic waves in bubbly liquids

Abstract

In this note we analyze some qualitative aspects of the solutions of the system of acoustic waves in bubbly liquids. In this sense we show uniqueness and continuous dependence of solutions for the general case. We also prove the exponential decay of solutions of the one-dimensional problem and a spatial decay estimate for the general three-dimensional case. We show how to extend the arguments and results to the case of the one-dimensional non-classical heat conduction in periodic heterogeneous materials.