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Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes. (English) Zbl 1246.35125
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 F. Lagouti√®re, N. Seguin and 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.

MSC:
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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