Validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws |
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Authors: | Gui-Qiang Chen,Sté phane Junca |
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Affiliation: | a Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, USA b IUFM & Université de Nice, UMR CNRS 6621, Parc Valrose, 06108, Nice, France c Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, 06108, Nice, France |
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Abstract: | Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L1-stability. New multidimensional features are recognized, especially including nonlinear propagations of oscillations with high frequencies. The validity of nonlinear geometric optics for entropy solutions in L∞ of multidimensional scalar conservation laws is justified. |
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Keywords: | primary: 35B40, 35L65 secondary: 35B35 |
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