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| Titel: |
Finite volume schemes for nonlinear parabolic problems: another regularization method |
| Auteur: |
R. Eymard T. Gallouet R. Herbin |
| Verschenen in: |
Acta mathematica Universitatis Comenianae |
| Paginering: | Jaargang LXXVI (2007) nr. 1 pagina's 3-10 |
| Jaar: |
2007 |
| Inhoud: |
On one hand, the existence of a solution to degenerate parabolic equations, without anonlinear convection term, can be proven using the results of Alt and Luckhaus, Minty and Kolmogorov. On the other hand, the proof of uniqueness of an entropy weak solutionto a nonlinear scalar hyperbolic equation,first provided by Krushkov, has been extended in two directions: Carrillo has handled the case of degenerate parabolic equations including a nonlinear convection term, whereasDi Perna has proven the uniqueness of weaker solutions, namely Young measure entropy solutions.All of these results are reviewed in the course of a convergence result for two regularizations of a degenerate parabolic problem including a nonlinear convective term. The first regularization is classicaly obtained by adding a minimal diffusion, the second one is given by a finite volume scheme on unstructured meshes. The convergence result istherefore only based on <i>L</i><sup><FONT SIZE='3' FACE='Symbol'>¥</FONT></sup>(<FONT SIZE='3' FACE='Symbol'>W</FONT><FONT SIZE='3' FACE='Symbol'>´</FONT>(0,<i>T</i>)) and <i>L</i><sup>2</sup>(0,<i>T; H</i><sup>1</sup>(<FONT SIZE='3' FACE='Symbol'>W</FONT>)) estimates, associated with the uniqueness result for aweaker sense for a solution. |
| Uitgever: |
Acta Mathematica Universitatis Comenianae, Institute of Applied Mathematics (provided by DOAJ) |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 18 van 68 gevonden artikelen
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