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

Di Perna, Ronald J.

Trans. Am. Math. Soc. 292, 383-420 (1985).

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.

Reviewer: M.Kopáčková-Suchá

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

Keywords:

entropy pair; Dirac mass; oscillations; weakly convergent; conservation laws; Tartar-Murat theory; compensated compactness; Young measure; compressible fluid dynamics; compressible elastostatics; transonic flow