Extinction for a Singular Diffusion Equation with Strong Gradient Absorption Revisited
Keyword(s):
The One
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AbstractWhen {2N/(N+1)<p<2} and {0<q<p/2}, non-negative solutions to the singular diffusion equation with gradient absorption\partial_{t}u-\Delta_{p}u+|\nabla u|^{q}=0\quad\text{in }(0,\infty)\times% \mathbb{R}^{N}vanish after a finite time. This phenomenon is usually referred to as finite-time extinction and takes place provided the initial condition {u_{0}} decays sufficiently rapidly as {|x|\to\infty}. On the one hand, the optimal decay of {u_{0}} at infinity guaranteeing the occurrence of finite-time extinction is identified. On the other hand, assuming further that {p-1<q<p/2}, optimal extinction rates near the extinction time are derived.
1997 ◽
Vol 139
(1)
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pp. 83-98
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2015 ◽
Vol 40
(5)
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pp. 897-917
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2004 ◽
Vol 17
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pp. 561-567
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2011 ◽
Vol 36
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pp. 961-975
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Keyword(s):
2014 ◽
Vol 21
(6)
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pp. 1435-1449
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