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Global classical solutions to partially dissipative quasilinear hyperbolic systems

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Abstract

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems. Under the assumption that the system is weakly dissipative, Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch. Rational Mech. Anal., Vol. 169, 2003, pp. 89–117). The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

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Authors and Affiliations

  1. Key Laboratory of Mathematics for Nonlinear Sciences, Ministry of Education, China; Shanghai Key Laboratory for Contemporary Applied Mathematics; School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Yi Zhou

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  1. Yi Zhou
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Correspondence to Yi Zhou.

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Project supported by the National Natural Science Foundation of China (No. 10728101), the Basic Research Program of China (No. 2007CB814800), the Doctoral Program Foundation of the Ministry of Education of China, the “111” Project (No. B08018) and SGST (No. 09DZ2272900).

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Zhou, Y. Global classical solutions to partially dissipative quasilinear hyperbolic systems. Chin. Ann. Math. Ser. B 32, 771–780 (2011). https://doi.org/10.1007/s11401-011-0666-z

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  • DOI: https://doi.org/10.1007/s11401-011-0666-z

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