The Compensated Compactness Method Applied to Systems of Conservation Laws
Chapter
Abstract
One of the main difficulties in solving nonlinear partial differential equations lies in the following fact: after introducing a suitable sequence of approximations one needs enough a priori estimates to ensure the convergence of a subsequence to a solution; this argument is based on compactness results and in a nonlinear case one needs more estimates than in the linear case where weak continuity results can be used.
Keywords
Weak Convergence Hyperbolic System Nonlinear Partial Differential Equation Nonlinear Elasticity Entropy Condition
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References
- [1]Dacorogna, B.: 1982, ‘Weak semicontinuity and weak lower semicontinuity of nonlinear functionals’, Lecture Notes in Mathematics, No. 922, Springer.Google Scholar
- [2]DiPerna, R.J.: Convergence of approximate solutions to conservation laws, to appear.Google Scholar
- [3]Tartar, L.C.: 1979, ‘Compensated compactness and applications to partial differential equations’, in Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, IV, pp. 136–192. Research Notes in Mathematics, Pitman.Google Scholar
Copyright information
© D. Reidel Publishing Company 1983