Front tracking approximations for slow erosion
| Autor: | Debora Amadori, Wen Shen |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Granular flow
Mathematical optimization Conservation law Applied Mathematics Granular flow slow erosion conservation laws front tracking existence and uniqueness of BV solutions existence and uniqueness of BV solutions Non local front tracking Discrete Mathematics and Combinatorics Applied mathematics Initial value problem A priori and a posteriori slow erosion conservation laws Analysis Mathematics |
| Zdroj: | Discrete & Continuous Dynamical Systems - A. 32:1481-1502 |
| ISSN: | 1553-5231 |
| DOI: | 10.3934/dcds.2012.32.1481 |
| Popis: | In this paper we study an integro-differential equation describing slow erosion, in a model of granular flow. In this equation the flux is non local and depends on $x$, $t$. We define approximate solutions by using a front tracking technique, adapted to this special equation. Convergence of the approximate solutions is established by means of suitable a priori estimates. In turn, these yield the global existence of entropy solutions in BV. Such entropy solutions are shown to be unique. We also prove the continuous dependence on initial data and on the erosion function, for the approximate as well as for the exact solutions. This establishes the well-posedness of the Cauchy problem. |
| Databáze: | OpenAIRE |
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