The Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory and numerical analysis

Abstract

In this paper, we establish the global well-posedness of the Cauchy problem for a generalised viscous Burgers equation with spatially decaying sound speed, continuing from part I of this series of papers. Moreover, we establish qualitative properties, specifically bounds and monotonicity properties of solutions to the Cauchy problem. We also establish a conditional convergence result for an explicit mid-point finite difference scheme used throughout part I to approximate solutions to the Cauchy problem.