Title: | Generalized solutions to the porous medium equation Huokoisen aineen yhtälön yleistetyt ratkaisut |
Author(s): | Lehtelä, Pekka |
Date: | 2018 |
Language: | en |
Pages: | 50 + app. 118 |
Department: | Matematiikan ja systeemianalyysin laitos Department of Mathematics and Systems Analysis |
ISBN: | 978-952-60-7978-3 (electronic) 978-952-60-7977-6 (printed) |
Series: | Aalto University publication series DOCTORAL DISSERTATIONS, 85/2018 |
ISSN: | 1799-4942 (electronic) 1799-4934 (printed) 1799-4934 (ISSN-L) |
Supervising professor(s): | Kinnunen, Juha, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland |
Thesis advisor(s): | Kinnunen, Juha, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland |
Subject: | Mathematics |
Keywords: | porous medium equation, weak solution, weak supersolution, supercaloric function, comparison principle, weak Harnack estimate, obstacle problem, huokoisen aineen yhtälö, heikko ratkaisu, heikko superratkaisu, superkalorinen funktio, vertailuperiaate, heikko Harnack-estimaatti, esteongelma |
Archive | yes |
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Abstract:Väitöskirjassa tutkitaan huokoisen aineen yhtälön yleistettyjen ratkaisuiden käsitteitä. Keskeinen tutkimuskysymys on ratkaisuiden ja superratkaisuiden määritelmien luokittelu ja ratkaisuluokkien välisten yhteyksien määrittäminen. |
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Parts:[Publication 1]: Pekka Lehtelä, Teemu Lukkari. The equivalence of weak and very weak supersolutions to the porous medium equation. Accepted for publication in The Tohoku Mathematical Journal, 23 pages, May 2016.[Publication 2]: Pekka Lehtelä. A weak Harnack estimate for supersolutions to the porous medium equation. Differential and Integral Equations, Volume 30, Number 11/12, pp 879–916, November/December 2017.[Publication 3]: Juha Kinnunen, Pekka Lehtelä, Peter Lindqvist and Mikko Parviainen. Supercaloric functions for the porous medium equation. Submitted to a journal, 21 pages, Available at arXiv:1801.04121, December 2017.[Publication 4]: Verena Bögelein, Pekka Lehtelä and Stefan Sturm. Regularity of weak solutions and supersolutions to the porous medium equation. Submitted to a journal, 23 pages, Available at arXiv:1801.05249, January 2018. |
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