Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes
The authors define entropy weak solutions and establish well-posedness for the Cauchy problem for the Burgers equation with a resonant singular source term. The interpretation of the non-conservative product in the source term follows the analysis of \textit{F. Lagoutière, N. Seguin} and \textit{T. Takahashi} [J. Differ. Equations 245, No. 11, 3503--3544 (2008; Zbl 1151.76033)]. For proving existence and for practical computation of solutions, the authors construct a finite volume scheme, which turns out to be a well-balanced scheme and which allows a simple and efficient treatment of the interface coupling. Numerical illustrations are given.
scientific article; zbMATH DE number 6039430