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- W1519919767 abstract "We obtain upper bounds for the quenching time of the solutions of the nonlocal parabolic MEMS equation $u_t=Delta u+lam/(1-u)^2(1+chiint_{Omega}1/(1-u) dx)^2$ in $Omegatimes (0,infty)$, $u=0$ on $1Omegatimes (0,infty)$, $u(x,0)=u_0$ in $Omega$, when $lambda$ is large. We prove the compactness of the quenching set under a mild condition on the initial data. When $Omega=B_R$ and $u_0$ is radially symmetric and monotone decreasing in $0le rle R$, we prove that the point $x=0$ is the only possible quenching set. When $u_0$ also satisfies some strict concavity assumption, we prove that for any $betain (2,3)$ the solution satisfies $1-u(x,t)ge C|x|^{frac{2}{beta}}$ for some constant $C>0$ and we also obtain the quenching time estimate in this case." @default.
- W1519919767 created "2016-06-24" @default.
- W1519919767 creator A5036827550 @default.
- W1519919767 date "2009-08-09" @default.
- W1519919767 modified "2023-09-27" @default.
- W1519919767 title "Quenching behaviour of a nonlocal parabolic MEMS equation" @default.
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