Well-posedness and self-similar asymptotics for a thin-film equation
dc.contributor.author | Gnann, Manuel V. | |
dc.date.accessioned | 2016-02-17T21:10:24Z | |
dc.date.available | 2016-02-17T21:10:24Z | |
dc.date.issued | 2015-07-30 | |
dc.identifier.citation | SIAM J. Math. Anal., 47(4), 2868–2902. | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/117366 | |
dc.description.abstract | We investigate compactly supported solutions for a thin-film equation with linear mobility in the regime of perfect wetting. This problem has already been addressed by Carrillo and Toscani, proving that the source-type self-similar profile is a global attractor of entropy solutions with compactly supported initial data. Here we study small perturbations of source-type self-similar solutions for the corresponding classical free boundary problem and set up a global existence and uniqueness theory within weighted L2-spaces under minimal assumptions. Furthermore, we derive asymptotics for the evolution of the solution, the free boundary, and the center of mass. As spatial translations are scaled out in our reference frame, the rate of convergence is higher than the one obtained by Carrillo and Toscani. | en_US |
dc.description.sponsorship | Funding of this work was provided by the International Max Planck Research School (IMPRS) of the Max Planck Institute for Mathematics in the Sciences (MPI MIS) in Leipzig and the Fields Institute in Toronto. The author’s research was partially supported by the National Science Foundation under grant NSF DMS-1054115. | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.relation.ispartofseries | Volume 47, Issue 4 | en_US |
dc.title | Well-posedness and self-similar asymptotics for a thin-film equation | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbtoplevel | Science | |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/117366/1/Gnann_2015.pdf | |
dc.identifier.doi | 10.1137/14099190X | |
dc.identifier.source | SIAM Journal on Mathematical Analysis | en_US |
dc.identifier.orcid | 0000-0002-1479-0387 | en_US |
dc.description.filedescription | Description of Gnann_2015.pdf : Main article (published version) | |
dc.identifier.name-orcid | Gnann, Manuel; 0000-0002-1479-0387 | en_US |
dc.owningcollname | Mathematics, Department of |
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