QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS
dc.date.accessioned | 2013-03-12T08:17:03Z | |
dc.date.available | 2013-03-12T08:17:03Z | |
dc.date.issued | 2004 | en_US |
dc.date.submitted | 2009-11-30 | en_US |
dc.identifier.uri | http://hdl.handle.net/10852/10626 | |
dc.description.abstract | We study the well-posedness of discontinuous entropy solutions to quasilinear aniso-tropic degenerate parabolic equations with explicit $(t,x)$--dependence: $$ \pt u + \si \pxi f_i(u,t,x)=\sij \pxj\left(\aij(u,t,x)\pxi u\right), $$ where $a(u,t,x)=(\aij(u,t,x))=\sa(u,t,x)\sa(u,t,x)^\top$ is nonnegative definite and each $x\mapsto f_i(u,t,x)$ is Lipschitz continuous. We establish a well-posedness theory for the Cauchy problem for such degenerate parabolic equations via Kruzkov's device of doubling variables, provided $\sa(u,t,\cdot)\in W^{2,\infty}$ for the general case and the weaker condition $\sa(u,t,\cdot)\in W^{1,\infty}$ for the case that $a$ is a diagonal matrix. We also establish a continuous dependence estimate for perturbations of the diffusion and convection functions. | eng |
dc.language.iso | eng | en_US |
dc.publisher | Matematisk Institutt, Universitetet i Oslo | |
dc.relation.ispartof | Preprint series. Pure mathematics http://urn.nb.no/URN:NBN:no-8076 | en_US |
dc.relation.uri | http://urn.nb.no/URN:NBN:no-8076 | |
dc.rights | © The Author(s) (2004). This material is protected by copyright law. Without explicit authorisation, reproduction is only allowed in so far as it is permitted by law or by agreement with a collecting society. | |
dc.title | QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS | en_US |
dc.type | Research report | en_US |
dc.date.updated | 2009-11-30 | en_US |
dc.rights.holder | Copyright 2004 The Author(s) | |
dc.creator.author | Chen, Gui-Qiang | en_US |
dc.creator.author | Karlsen, Kenneth H. | en_US |
dc.subject.nsi | VDP::410 | en_US |
dc.identifier.urn | URN:NBN:no-23679 | en_US |
dc.type.document | Forskningsrapport | en_US |
dc.identifier.duo | 97473 | en_US |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/10626/1/pm31-04.pdf |
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