Turkish Journal of Mathematics and Computer Science

Yazarlar: Burhan Selçuk, Nuri Özalp

Konular:Mühendislik

Anahtar Kelimeler:Heat equation,Nonlinear diffusion equation,Nonlinear boundary condition,Quenching,Maximum principles

Özet: In this paper, we study a nonlinear diffusion equation (φ(u))_{t}=u_{xx}, 00 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.

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