An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by "weaker than weak" solutions of the Riemann problem

研究成果: 雜誌貢獻期刊論文同行評審

25 引文 斯高帕斯(Scopus)

摘要

We construct a generalized solution of the Riemann problem for strictly hyperbolic systems of conservation laws with source terms, and we use this to show that Glimm's method can be used directly to establish the existence of solutions of the Cauchy problem. The source terms are taken to be of the form a′ G, and this enables us to extend the method introduced by Lax to construct general solutions of the Riemann problem. Our generalized solution of the Riemann problem is "weaker than weak" in the sense that it is weaker than a distributional solution. Thus, we prove that a weak solution of the Cauchy problem is the limit of a sequence of Glimm scheme approximate solutions that are based on "weaker than weak" solutions of the Riemann problem. By establishing the convergence of Glimm's method, it follows that all of the results on time asymptotics and uniqueness for Glimm's method (in the presence of a linearly degenerate field) now apply, unchanged, to inhomogeneous systems.

原文???core.languages.en_GB???
頁(從 - 到)515-549
頁數35
期刊Journal of Differential Equations
222
發行號2
DOIs
出版狀態已出版 - 15 3月 2006

指紋

深入研究「An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by "weaker than weak" solutions of the Riemann problem」主題。共同形成了獨特的指紋。

引用此