Blow up and quenching for a problem with nonlinear boundary conditions

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dc.contributor.authorOzalp, N.
dc.contributor.authorSelcuk, B.
dc.date.accessioned2024-09-29T16:21:24Z
dc.date.available2024-09-29T16:21:24Z
dc.date.issued2015
dc.departmentKarabük Üniversitesien_US
dc.description.abstractIn this article, we study the blow up behavior of the heat equation ut = uxx with ux(0, t) = up(0, t), up(0, t) = ux(a, t). We also study the quenching behavior of the nonlinear parabolic equation vt = vxx +2v2x =(1-v) with vx(0, t) = (1 - v(0, t))-p+2, vx(a, t) = (1 v(a; t))-q+2. In the blow up problem, if u0 is a lower solution then we get the blow up occurs in a finite time at the boundary x = a and using positive steady state we give criteria for blow up and non-blow up. In the quenching problem, we show that the only quenching point is x = a and vt blows up at the quenching time, under certain conditions and using positive steady state we give criteria for quenching and non-quenching. These analysis is based on the equivalence between the blow up and the quenching for these two equations. © 2015 Texas State University - San Marcos.en_US
dc.identifier.issn1072-6691
dc.identifier.scopus2-s2.0-84937704681en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.urihttps://hdl.handle.net/20.500.14619/9748
dc.identifier.volume2015en_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherTexas State University - San Marcosen_US
dc.relation.ispartofElectronic Journal of Differential Equationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBlow upen_US
dc.subjectHeat equationen_US
dc.subjectMaximum principleen_US
dc.subjectNonlinear boundary conditionen_US
dc.subjectNonlinear parabolic equationen_US
dc.subjectQuenchingen_US
dc.titleBlow up and quenching for a problem with nonlinear boundary conditionsen_US
dc.typeArticleen_US

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