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Analysis and approximation of conservation laws with source terms. (English) Zbl 0888.65100
A new Lax-type formula for the solution of Riemann problems is derived for conservation laws \(u_t+ f(u)_x= a_x\) with \(f\) being an even convex function and \(a(\cdot)\) a bounded piecewise smooth source term. For fixed source term the evolutionary operator associated with the conservation law is an \(L^1\) contraction so that existence of solutions can be proven for weak solutions. A Godunov-type finite difference scheme is constructed which can be shown to be \(L^\infty\) stable.
Reviewer: Th.Sonar (Hamburg)

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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