Mathematical Society of the Rep. of China;Mathematical Society of the Republic of China
Abstract:
摘要： We give a new approach of constructing the generalized entropy solutions to the Riemann problem of scalar nonlinear balance laws with singular source terms. The source term is singular in the sense that it is a product of delta function and a discontinuous function, which is undefined in distribution. By re-formulating the source term, we study the corresponding perturbed Riemann problem. The existence and stability of perturbed Riemann solutions is established under some entropy condition so that the generalized entropy solutions of Riemann problem can be interpreted as the limit of corresponding perturbed Riemann solutions. The self-similarity of generalized entropy solutions is also obtained, which means that Lax's method in [13] can be extended to scalar nonlinear balance laws with singular source terms. 2010Mathematics Subject Classification: 35L60, 35L65, 35L67. Key words and phrases: Conservation laws, Nonlinear balance laws, Riemann problems, Perturbed Riemann problems, Characteristic method, Lax's method. 出版者： Mathematical Society of the Republic of China 出版日期： 2013-04-01 出處： Taiwanese journal of mathematics, 2013-04, Vol.17 (2), p.431-464 資源來源： JSTOR Arts & Sciences XV 版權： 2013 Mathematical Society of the Republic of China 識別號： ISSN: 1027-5487 識別號： ISSN: 2224-6851 識別號： EISSN: 2224-6851 識別號： DOI: 10.11650/tjm.17.2013.2296
