The nonlinear initial-boundary value problem and the existence of multidimensional shock wave for quasilinear hyperbolic-parabolic coupled systems

zbMath0678.35071MaRDI QIDQ1124052

Dening Li

Publication date: 1987

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

zbMATH Keywords

existenceinitial-boundary value problemCauchy problemshock wavequasilinearRankine-Hugoniot conditiondiscontinuous initial datazero initial conditionhyperbolic-parabolic coupled systemKreiss hyperbolic operatorPetrovsky parabolic operatorsmooth initial valuesuniquess

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Shocks and singularities for hyperbolic equations (35L67) Initial-boundary value problems for second-order parabolic equations (35K20) First-order nonlinear hyperbolic equations (35L60) Initial-boundary value problems for first-order hyperbolic systems (35L50) Initial value problems for second-order parabolic equations (35K15) Initial value problems for first-order hyperbolic systems (35L45) Partial differential equations of mixed type and mixed-type systems of partial differential equations (35M99)

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