Complete quenching phenomenon and instantaneous shrinking of support of solutions of degenerate parabolic equations with nonlinear singular absorption
2019 ◽
Vol 149
(5)
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pp. 1323-1346
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Keyword(s):
The One
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AbstractThis paper deals with nonnegative solutions of the one-dimensional degenerate parabolic equations with zero homogeneous Dirichlet boundary condition. To obtain an existence result, we prove a sharp estimate for |ux|. Besides, we investigate the qualitative behaviours of nonnegative solutions such as the quenching phenomenon, and the finite speed of propagation. Our results of the Dirichlet problem are also extended to the associated Cauchy problem on the whole domain ℝ. In addition, we also consider the instantaneous shrinking of compact support of nonnegative solutions.
2015 ◽
Vol 47
(3)
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pp. 2426-2441
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2000 ◽
Vol 130
(4)
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pp. 877-908
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1996 ◽
Vol 203
(1)
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pp. 78-103
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2008 ◽
Vol 143
(1)
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pp. 1-15
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2020 ◽
Vol 25
(10)
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pp. 3963-3981
Keyword(s):
1998 ◽
Vol 50
(1)
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pp. 119-138
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