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Dependence of entropy solutions in the large for the Euler equations on nonlinear flux functions.(English)Zbl 1133.35066

The authors consider the Cauchy problem for a nonlinear hyperbolic system of conservation laws with one spatial variable. The flux functions depend on the parameter vector. The dependence of entropy solutions in the large on the parameter vector is studied. The authors formulate an approach for establishing the \(L_1\)-estimates pointwise in time with respect to entropy solutions for zero and non-zero parameter vector. The approach is applied for some nonlinear physical systems, including the isentropic, relativistic, and isothermal Euler systems.

MSC:

35L65 Hyperbolic conservation laws
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
76N15 Gas dynamics (general theory)
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35B35 Stability in context of PDEs
83A05 Special relativity
35L45 Initial value problems for first-order hyperbolic systems

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