Selcuk, B.Ozalp, N.2024-09-292024-09-2920151072-6691https://hdl.handle.net/20.500.14619/9747In this article, we study the quenching behavior of solution to the semilinear heat equation (Formula presented) with f(v) = u-r or (1 – v)–r and (Formula presented) For this, we utilize the quenching problem ut=uxx with ux(0,t)=u-p(0,t), ux(a,t)=(1-u(a,t))-q. In the second problem, if u0 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 utblows 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 v0 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 vt blows up at quenching time. © 2015 Texas State University.eninfo:eu-repo/semantics/closedAccessHeat equationMaximum principleMonotone iterationQuenchingSingular boundary conditionArticle2-s2.0-84950984473Q32015