## 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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