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Zbl 0703.35032
Marcati, Pierangelo
Convergence of approximate solutions to scalar conservation laws by degenerate diffusion. (English)
[J] Rend. Semin. Mat. Univ. Padova 81, 65-78 (1989). ISSN 0041-8994

This paper is concerned with the existence of weak solutions to the scalar conservation laws $$ (*)\quad u\sb t+f(u)\sb x=0,\quad x\in {\bbfR},\quad t>0,\quad u(x,0)=u\sb 0(x), $$ in the framework provided by compensated compactness. The author shows that the unique weak `entropic' solution to (*) can be obtained by replacing the usual viscous approximation by means of the porous media operator.
[V.Lakshmikantham]

MSC 2000:: *35D05 Existence of generalized solutions of PDE
35L65 Conservation laws
65M99 Numerical methods for IVP of PDE
65N99 Numerical methods for BVP of PDE
35K57 Reaction-diffusion equations

Keywords: existence of weak solutions; scalar conservation laws; compensated compactness

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