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Beauregard","submitted_at":"2019-07-08T18:22:12Z","abstract_excerpt":"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 $r=2$. 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