頁籤選單縮合
題 名 | Existence and Uniqueness of Lax-type Solutions to the Riemann Problem of Scalar Balance Law with Singular Source Term |
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作 者 | 張淵; 周世偉; 洪盟凱; 林英杰; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 17:2 2013.04[民102.04] |
頁 次 | 頁431-464 |
分類號 | 310 |
關鍵詞 | Conservation laws; Nonlinear balance laws; Riemann problems; Perturbed Riemann problems; Characteristic method; Lax's method; |
語 文 | 英文(English) |
英文摘要 | 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. |
本系統中英文摘要資訊取自各篇刊載內容。