Existence and Strong Pre-compactness Properties for Entropy Solutions of a First-Order Quasilinear Equation with Discontinuous Flux |
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| Authors: | E. Yu. Panov |
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| Affiliation: | (1) Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA;(2) Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA |
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| Abstract: | Sequences of entropy solutions of a non-degenerate first-order quasilinear equation are shown to be strongly pre-compact in the general case of a Caratheodory flux vector. Existence of the weak and entropy solution to the Cauchy problem for such an evolutionary equation is also established. The proofs are based on the general localization principle for H-measures corresponding to sequences of measure-valued functions. |
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