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Compensated compactness and general systems of conservation laws. (English) Zbl 0606.35052

The author outlines a general program and presents some new results dealing with oscillations in weakly convergent solution sequences to nonlinear systems of conservation laws of hyperbolic and elliptic type. Weak convergence is transformed into strong one using the Tartar-Murat theory of compensated compactness and the Young measure without using uniform bounds of derivatives. The equations of compressible fluid dynamics and of compressible elastostatics and small disturbance equation of transonic flow providing basic models for the general theory concerning hyperbolic elliptic and mixed type systems, respectively are dealt with as examples.

MSC:

35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics
35J60 Nonlinear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
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