Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.advisor Londen, Stig-Olof, Prof. Pulkkinen, Aappo 2012-08-30T06:29:27Z 2012-08-30T06:29:27Z 2011
dc.identifier.isbn 978-952-60-4139-1 (PDF)
dc.identifier.isbn 978-952-60-4138-4 (printed)
dc.identifier.issn 1799-4942
dc.description.abstract In this dissertation we study blow-up phenomena in semilinear parabolic equations with both exponential and power-type nonlinearities. We study the behavior of the solutions as the blow-up moment in time and the blow-up point in space are approached. Our focus is on the supercritical case; however, we also give some results on the subcritical case. We prove results concerning the blow-up rate of solutions, and we obtain the blow-up profile for limit L1-solutions both with respect to the similarity variables and at the blow-up moment. We use techniques that are applicable both for the exponential and power nonlinearities. We also consider immediate regularization for minimal L1-solutions and improve on some earlier results. We are also interested in the behavior of selfsimilar solutions and we prove the existence of regular selfsimilar solutions that intersect the singular one arbitrary number of times. en
dc.format.extent Verkkokirja (451 KB, 51 s.)
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Aalto University en
dc.relation.ispartofseries Aalto University publication series DOCTORAL DISSERTATIONS, 45/2011 en
dc.relation.haspart [Publication 1]: M. Fila, A. Pulkkinen, Backward selfsimilar solutions of supercritical parabolic equations, Applied Mathematics Letters 22 (2009), 897-901. © 2008 Elsevier Science. By permission. en
dc.relation.haspart [Publication 2]: M. Fila, A. Pulkkinen, Nonconstant selfsimilar blow-up profile for the exponential reaction-diffusion equation, Tohoku Mathematical Journal 60 (2008), 303-328. © 2008 Tohoku University, Mathematical Institute. By permission. en
dc.relation.haspart [Publication 3]: A. Pulkkinen, Blow-up profiles of solutions for the exponential reaction-diffusion equation, arXiv:1102.4158v1 [math.AP] (2011), 1-29, (accepted for publication in Mathematical Methods in the Applied Sciences). © 2011 by author. en
dc.relation.haspart [Publication 4]: A. Pulkkinen, Some comments concerning the blow-up of solutions of the exponential reaction-diffusion equation, arXiv:1102.4275v2 [math.AP] (2011), 1-18. © 2011 by author. en
dc.subject.other Mathematics
dc.title Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities en
dc.type G5 Artikkeliväitöskirja fi Perustieteiden korkeakoulu fi
dc.contributor.department Matematiikan ja systeemianalyysin laitos fi
dc.contributor.department Department of Mathematics and Systems Analysis en
dc.subject.keyword semilinear parabolic equation en
dc.subject.keyword supercritical case en
dc.subject.keyword exponential nonlinearity en
dc.subject.keyword power-type nonlinearity en
dc.subject.keyword blow-up en
dc.subject.keyword selfsimilar solutions en
dc.subject.keyword blow-up rate en
dc.subject.keyword blow-up profile en
dc.subject.keyword regularity en
dc.subject.keyword semigroup estimates en
dc.identifier.urn URN:ISBN:978-952-60-4139-1
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en
dc.contributor.supervisor Gripenberg, Gustaf, Prof.

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