Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions

Matthew A. Beauregard; Burhan Selcuk

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arXiv · 1907.03796

Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions

Matthew A. Beauregard·Burhan Selcuk

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Abstract

In this paper, the quenching behavior of the non-Newtonian filtration equation $(\phi (u))_{t}=(\left \vert u_{x}\right \vert ^{r-2}u_{x})_{x}$ with singular boundary conditions, $u_{x}\left( 0,t\right) =u^{-p}(0,t)$, $u_{x}\left( a,t\right) =(1-u(a,t))^{-q}$ is investigated. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined when $\phi(u)=u$ and $r=2$. Numerical experiments are provided to illustrate and provide additional validation of the theoretical estimates to the quenching rates and times.

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Matthew A. Beauregard, Burhan Selcuk. 2019-07-08. Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions. https://arxiv.org/abs/1907.03796

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