On a weak solution of certain system of conservation laws

概要

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We will consider the Cauchy problem for a system of conservation laws, and we are interested in the global existence of weak solutions of this problem. Though the Riemann problem for the system has been well studied, we do not know a general existence theorem of weak solutions for the Cauchy problem in a case where the initial functions are smooth, except several cases. As the existence of δ-shock has been recently studied, we will consider a system of conservation laws whose Riemann problem accepts a weak solution containing the δ-shock. In this paper we assume that the initial functions are in C^∞_0 (R^1), and prove that, if we may accept the notion of weak solution introduced by P. D. Lax, the Cauchy problem can not have a weak solution.
兵庫大学の論文
2007-03-31