Generalized solutions of an inhomogeneous inviscid Burgers equation

Abstract

We derive generalized solutions of an inhomogeneous inviscid Burgers equation using vanishing viscosity method. This is achieved with the classical solution of a concerned viscous inhomogeneous Burgers equation. We then study Riemann problem for a de-coupled system. The weak solutions of the system are explicitly obtained by Volpert product concept. There are infinitely many real valued solutions for the system in the case of rarefaction wave and the weak solutions consist of δ- measures in the case of shock wave. Motivated by the structure of weak solutions, we construct the explicit generalized solutions for a more general de-coupled system. © 2021, The Indian National Science Academy.