Ozalp, N.Selcuk, B.2024-09-292024-09-2920151072-6691https://hdl.handle.net/20.500.14619/9748In 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.eninfo:eu-repo/semantics/closedAccessBlow upHeat equationMaximum principleNonlinear boundary conditionNonlinear parabolic equationQuenchingArticle2-s2.0-84937704681Q32015