A geometric study of shocks in equations that change type |
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Authors: | Barbara Lee Keyfitz Milton da Costa Lopes-Filho |
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Institution: | (1) Mathematics Department, University of Houston, 4800 Calhoun Street, 77204-3476 Houston, Texas;(2) Departamento de Matemática, IMECC-UNICAMP, Caixa Postal 6065, 13081-970 Campinas, SP, Brasil |
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Abstract: | In this paper we validate the generalized geometric entropy criterion for admissibility of shocks in systems which change type. This condition states that a shock between a state in a hyperbolic region and one in a nonhyperbolic region is admissible if the Lax geometric entropy criterion, based on the number of characteristics entering the shock, holds, where now the real part of a complex characteristic replaces the characteristic speed itself. We test this criterion by a nonlinear inviscid perturbation. We prove that the perturbed Cauchy problem in the elliptic region has a solution for a uniform time if the data lie in a suitable class of analytic functions and show that under small perturbations of the data a perturbed shock and a perturbed solution in the hyperbolic region exist, also for a uniform time. |
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Keywords: | Hyperbolic conservation laws change of type shock stability shock perturbation geometric entropy criterion |
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