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Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. (English) Zbl 1037.35041
The authors consider the Cauchy problem for a general one-dimensional \(n\times n\) hyperbolic symmetrizable system of balance laws. The main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions. They propose a general framework for this kind of problems by introducing an entropy variable, and prove some general statements about the global existence of a smooth solution under different sets of conditions. The main tool in this paper is a refined energy estimate and the application of a suitable version of the Kawashima condition.

MSC:
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
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