blow up and quenching for a problem with nonlinear boundary conditions

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ID: 135313
2015
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Ranked #99 of 219 articles by views in icsoft 2006 - 1st international conference on software and data technologies, proceedings

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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.
Reference Key
ozalp2015electronicblow Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Nuri Ozalp;Burhan Selcuk
Journal icsoft 2006 - 1st international conference on software and data technologies, proceedings
Year 2015
DOI
DOI not found
URL
http://ejde.math.txstate.edu/Volumes/2015/192/abstr.html
Keywords Keywords not found

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