Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

Year 2018, Volume: 8, 65 - 69, 30.06.2018

Burhan Selçuk , Nuri Özalp

Abstract

In this paper, we study a nonlinear diffusion equation (φ(u))_{t}=u_{xx}, 0<x<a, t>0 with singular boundary outfluxes u_{x}(0,t)=u^{-p}(0,t), u_{x}(a,t)=-u^{-q}(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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