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.
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References
Dacorogna, B.: 1982, ‘Weak semicontinuity and weak lower semicontinuity of nonlinear functionals’, Lecture Notes in Mathematics, No. 922, Springer.
DiPerna, R.J.: Convergence of approximate solutions to conservation laws, to appear.
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.
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© 1983 D. Reidel Publishing Company
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Tartar, L. (1983). The Compensated Compactness Method Applied to Systems of Conservation Laws. In: Ball, J.M. (eds) Systems of Nonlinear Partial Differential Equations. NATO Science Series C: (closed), vol 111. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7189-9_13
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DOI: https://doi.org/10.1007/978-94-009-7189-9_13
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