Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

Authors : Burhan Selçuk, Nuri Özalp

Pages : 65-69

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Publication Date : 2018-06-30

Article Type : Research Paper

Abstract :In this paper, we study a nonlinear diffusion equation insert ignore into journalissuearticles values(φinsert ignore into journalissuearticles values(u););_{t}=u_{xx}, 00 with singular boundary outfluxes u_{x}insert ignore into journalissuearticles values(0,t);=u^{-p}insert ignore into journalissuearticles values(0,t);, u_{x}insert ignore into journalissuearticles values(a,t);=-u^{-q}insert ignore into journalissuearticles values(a,t);. Firstly, we get the quenchnig occurs in a finite time at the boundary x=a under certain conditions. Finally, we show the time derivative blows up at the quenching time and we also establish results on quenching time and rate for certain nonlinearities.
Keywords : Heat equation, Nonlinear diffusion equation, nonlinear boundary condition, quenching, maximum principles

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