BLOW UP AND QUENCHING FOR A PROBLEM WITH NONLINEAR BOUNDARY CONDITIONS
| dc.authorid | Selcuk, Burhan/0000-0002-5141-5148 | |
| dc.authorid | OZALP, Nuri/0000-0002-8028-3391 | |
| dc.contributor.author | Ozalp, Nuri | |
| dc.contributor.author | Selcuk, Burhan | |
| dc.date.accessioned | 2024-09-29T16:11:24Z | |
| dc.date.available | 2024-09-29T16:11:24Z | |
| dc.date.issued | 2015 | |
| dc.department | Karabük Üniversitesi | en_US |
| dc.description.abstract | In this article, we study the blow up behavior of the heat equation u(t) = u(xx) with u(x) (0, t) = u(p) (0,t), u(x) (a,t) = u(q) (a,t). We also study the quenching behavior of the nonlinear parabolic equation v(t) = v(xx) +2v(x)(2) /(1-v) with v(x)(0,t) = (1-v(0, t))(-p+2), v(x)(a,t) = (1-v (a, t)(-q+2). In the blow up problem, if u(0) 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 v(t) 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. | en_US |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14619/8420 | |
| dc.identifier.wos | WOS:000358263400003 | en_US |
| dc.identifier.wosquality | Q2 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Texas State Univ | en_US |
| dc.relation.ispartof | Electronic Journal of Differential Equations | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Heat equation | en_US |
| dc.subject | nonlinear parabolic equation | en_US |
| dc.subject | blow up | en_US |
| dc.subject | nonlinear boundary condition | en_US |
| dc.subject | quenching | en_US |
| dc.subject | maximum principle | en_US |
| dc.title | BLOW UP AND QUENCHING FOR A PROBLEM WITH NONLINEAR BOUNDARY CONDITIONS | en_US |
| dc.type | Article | en_US |
