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Well-posedness results for triply nonlinear degenerate parabolic equations.
hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
dc.contributor.author | ANDREIANOV, Boris | |
hal.structure.identifier | Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | BENDAHMANE, Mostafa | |
hal.structure.identifier | Center of Mathematics for Applications [Oslo] [CMA] | |
dc.contributor.author | KARLSEN, Kenneth Hvistendahl | |
hal.structure.identifier | LAME Ouagadougou, Burkina-Faso [LAME] | |
dc.contributor.author | OUARO, Stanislas | |
dc.date.accessioned | 2024-04-04T02:29:07Z | |
dc.date.available | 2024-04-04T02:29:07Z | |
dc.date.issued | 2009 | |
dc.identifier.issn | 0022-0396 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190149 | |
dc.description.abstractEn | We study well-posedness of triply nonlinear degenerate elliptic–parabolic–hyperbolic problems of the kind b(u)t −div a(u,∇φ(u))+ ψ(u) = f , u|t=0 = u0 in a bounded domain with homogeneous Dirichlet boundary conditions. The nonlinearities b,φ and ψ are supposed to be continuous non-decreasing, and the nonlinearity ˜a falls within the Leray–Lions framework. Some restrictions are imposed on the dependence of a(u,∇φ(u)) on u and also on the set where φ degenerates. A model case is a(u,∇φ(u)) = f(b(u),ψ(u),φ(u)) + k(u)a0(∇φ(u)), with a nonlinearity φ which is strictly increasing except on a locally finite number of segments, and the nonlinearity a0 which is of the Leray–Lions kind. We are interested in existence, uniqueness and stability of L∞ entropy solutions. For the parabolic–hyperbolic equation (b = Id), we obtain a general continuous dependence result on data u0, f and nonlinearities b,ψ,φ, a. Similar result is shown for the degenerate elliptic problem, which corresponds to the case of b ≡ 0 and general non-decreasing surjective ψ. Existence, uniqueness and continuous dependence on data u0, f are shown in more generality. For instance, the assumptions [b + ψ](R) = R and the continuity of φ ◦([b + ψ]^{−1}) permit to achieve the well-posedness result for bounded entropy solutions of this triply nonlinear evolution problem. | |
dc.language.iso | en | |
dc.publisher | Elsevier | |
dc.subject | Degenerate hyperbolic–parabolic equation | |
dc.subject | Conservation law | |
dc.subject | Leray–Lions type operator | |
dc.subject | Non-Lipschitz flux | |
dc.subject | Entropy solution | |
dc.subject | Existence | |
dc.subject | Uniqueness | |
dc.subject | Stability | |
dc.title.en | Well-posedness results for triply nonlinear degenerate parabolic equations. | |
dc.type | Article de revue | |
dc.identifier.doi | 10.1016/j.jde.2009.03.001 | |
dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
dc.identifier.arxiv | 0810.2326 | |
bordeaux.journal | Journal of Differential Equations | |
bordeaux.page | 277–302 | |
bordeaux.volume | 247 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 1 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00475758 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00475758v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2009&rft.volume=247&rft.issue=1&rft.spage=277%E2%80%93302&rft.epage=277%E2%80%93302&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=ANDREIANOV,%20Boris&BENDAHMANE,%20Mostafa&KARLSEN,%20Kenneth%20Hvistendahl&OUARO,%20Stanislas&rft.genre=article |
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