Disappearance and global existence of interfaces for a doubly degenerate parabolic equation with variable coefficient |
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| Authors: | Nan Li Liangchen Wang Chunlai Mu Pan Zheng |
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| Affiliation: | 1. Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China |
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| Abstract: | This paper deals with the Cauchy problem for a doubly degenerate parabolic equation with variable coefficient ![urn:x-wiley:1704214:media:mma3157:mma3157-math-0001]( "urn:x-wiley:1704214:media:mma3157:mma3157-math-0001") For the case λ + 1 ≥ N, one proves that depending on the behavior of the variable coefficient at infinity, the Cauchy problem either possesses the property of finite speed of propagation of perturbation or the support blows up in finite time. This completes a result by Tedeev (A.F.Tedeev, The interface blow‐up phenomenon and local estimates for doubly degenerate parabolic equations, Appl. Anal. 86 (2007) 755–782.), which asserts the same result under the condition λ + 1 < N. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | doubly degenerate parabolic equation finite speed of propagation variable coefficient disappearance of interfaces global existence of interfaces subclass35K55 35B40 |
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