A nonlinear fourth-order parabolic equation and related logarithmic Sobolev inequalities

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dc.creatorDolbeault, J.
dc.creatorGentil, I.
dc.creatorJungel, A.
dc.date2004-09-15
dc.date.accessioned2026-07-07T05:12:08Z
dc.date.available2026-07-07T05:12:08Z
dc.descriptionA nonlinear fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions is shown. A criterion for the uniqueness of non-negative weak solutions is given. Finally, it is proved that the solution converges exponentially fast to its mean value in the ``entropy norm'' using a new optimal logarithmic Sobolev inequality for higher derivatives.
dc.identifierhttps://arxiv.org/abs/math/0409249
dc.identifierhttp://arxiv.org/abs/math/0409249
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72477
dc.subjectAnalysis of PDEs
dc.titleA nonlinear fourth-order parabolic equation and related logarithmic Sobolev inequalities
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