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Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity

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dc.contributor.authorFilippas, Stathis
dc.contributor.authorHerrero, Miguel A.
dc.contributor.authorVelázquez, J.J. L.
dc.date.accessioned2023-06-20T16:59:28Z
dc.date.available2023-06-20T16:59:28Z
dc.date.issued2000
dc.description.abstractWe consider the semilinear heat equation with critical power nonlinearity. Using formal. arguments based on matched asymptotic expansion techniques, we give a detailed description of radially symmetric sign-changing solutions, which blow-up at x = 0 and t = T < ∞, for space dimension N = 3,4,5,6. These solutions exhibit fast blow-up; i.e. they satisfy lim(t up arrowT)(T - t)(1/(p-1))u(0, t) = ∞. In contrast, radial solutions that are positive and decreasing behave as in the subcritical case for any N ≥ 3. This last result is extended in the case of exponential nonlinearity and N = 2.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16657
dc.identifier.doi10.1098/rspa.2000.0648
dc.identifier.issn1364-5021
dc.identifier.officialurlhttp://rspa.royalsocietypublishing.org/content/456/2004/2957.full.pdf+html
dc.identifier.relatedurlhttp://rspa.royalsocietypublishing.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57582
dc.journal.titleProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
dc.language.isoeng
dc.page.final2982
dc.page.initial2957
dc.publisherRoyal Society of London
dc.rights.accessRightsrestricted access
dc.subject.cdu536.2
dc.subject.cdu517.956.4
dc.subject.keywordMatched asymptotic expansions
dc.subject.keywordsemilinear heat equation
dc.subject.keywordblow-up
dc.subject.keywordcritical exponents
dc.subject.keywordsingularities
dc.subject.keyworddynamics
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleFast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
dc.typejournal article
dc.volume.number456
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