THE QUENCHING OF SOLUTIONS OF A REACTION–DIFFUSION EQUATION WITH FREE BOUNDARIES
2016 ◽
Vol 94
(1)
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pp. 110-120
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Keyword(s):
This paper concerns the quenching phenomena of a reaction–diffusion equation $u_{t}=u_{xx}+1/(1-u)$ in a one dimensional varying domain $[g(t),h(t)]$, where $g(t)$ and $h(t)$ are two free boundaries evolving by a Stefan condition. We prove that all solutions will quench regardless of the choice of initial data, and we also show that the quenching set is a compact subset of the initial occupying domain and that the two free boundaries remain bounded.
2020 ◽
Vol 484
(1)
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pp. 123666
2016 ◽
Vol 260
(5)
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pp. 3991-4015
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Keyword(s):
1995 ◽
Vol 125
(2)
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pp. 283-327
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2004 ◽
Vol 64
(5)
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pp. 507-520
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1975 ◽
Vol 27
(1-2)
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pp. 17-98
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2020 ◽
Vol 4
(4)
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pp. 137-146