QUENCHING BEHAVIOR OF SEMILINEAR HEAT EQUATIONS WITH SINGULAR BOUNDARY CONDITIONS
| dc.authorid | Selcuk, Burhan/0000-0002-5141-5148 | |
| dc.authorid | OZALP, Nuri/0000-0002-8028-3391 | |
| dc.contributor.author | Selcuk, Burhan | |
| dc.contributor.author | Ozalp, Nuri | |
| dc.date.accessioned | 2024-09-29T16:11:27Z | |
| dc.date.available | 2024-09-29T16:11:27Z | |
| dc.date.issued | 2015 | |
| dc.department | Karabük Üniversitesi | en_US |
| dc.description.abstract | In this article, we study the quenching behavior of solution to the semilinear heat equation v(t) = v(xx) + f (v), with f(v) = -v(-r) or (1 - v)(-r) and v(x)(0,t) = v(-P)(0,t), v(x)(a,t) = (1-v(a,t))(-q). For this, we utilize the quenching problem u(t) = u(xx) with u(x) (0, t) = u(-P)(0,t), u(x)(a,t) = (1 - u(a,t))(-q). In the second problem, if u(0) is an upper solution (a lower solution) then we show that quenching occurs in a finite time, the only quenching point is x = 0 (x = a) and u(t) blows up at quenching time. Further, we obtain a local solution by using positive steady state. In the first problem, we first obtain a local solution by using monotone iterations. Finally, for f(v) = -v(-r) ((1 - v)(-r)), if v(0) is an upper solution (a lower solution) then we show that quenching occurs in a finite time, the only quenching point is x = 0 (x = a) and v(t) blows up at quenching time. | en_US |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14619/8426 | |
| dc.identifier.wos | WOS:000367238900003 | 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 | singular boundary condition | en_US |
| dc.subject | quenching | en_US |
| dc.subject | maximum principle | en_US |
| dc.subject | monotone iteration | en_US |
| dc.title | QUENCHING BEHAVIOR OF SEMILINEAR HEAT EQUATIONS WITH SINGULAR BOUNDARY CONDITIONS | en_US |
| dc.type | Article | en_US |
