A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws
| Autor: | Alberto Tesei, Andrea Terracina, Flavia Smarrazzo, Michiel Bertsch |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Conservation law General Mathematics 010102 general mathematics Scalar (physics) Radon measure-valued solutions Mathematics::Analysis of PDEs entropy inequalities uniqueness 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs Settore MAT/05 - Analisi Matematica Bounded function Radon measure FOS: Mathematics First order hyperbolic conservation laws Initial value problem Uniqueness 0101 mathematics Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni (Online) 30 (2019): 137–168. doi:10.4171/RLM/839 info:cnr-pdr/source/autori:Bertsch M.; Smarrazzo F.; Terracina A.; Tesei A./titolo:A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws,/doi:10.4171%2FRLM%2F839/rivista:Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni (Online)/anno:2019/pagina_da:137/pagina_a:168/intervallo_pagine:137–168/volume:30 |
| DOI: | 10.4171/RLM/839 |
| Popis: | We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem $$ \begin{cases} u_t+[\varphi(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0 &\text{in } \mathbb{R}\times \{0\}, \end{cases} $$ where $u_0$ a positive Radon measure whose singular part is a finite superposition of Dirac masses, and $\varphi\in C^2([0,\infty))$ is bounded. The novelty of the paper is the introduction of a compatibility condition which, combined with standard entropy conditions, guarantees uniqueness. |
| Databáze: | OpenAIRE |
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