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Global existence of classical solutions to the Cauchy problem on a semi-bounded initial axis for quasilinear hyperbolic systems

✍ Scribed by Ta-Tsien Li; Libin B. Wang

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 243 KB
Volume: 56
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2003.10.022

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✦ Synopsis

In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Under the assumption that the leftmost (resp. rightmost) eigenvalue is weakly linearly degenerate, we obtain the global existence and uniqueness of C 1 solution with small and decaying initial data.

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## Abstract This work is a continuation of our previous work. In the present paper, we study the existence and uniqueness of global piecewise __C__^1^ solutions with shock waves to the generalized Riemann problem for general quasilinear hyperbolic systems of conservation laws with linear damping in