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The self-similar
profiles of generalized KPZ equation
Yuanwei Qi and Mingxin Wang |
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Vol. 201 (2001), No. 1, 223–240
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Abstract |
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In this paper we consider, for 1 ≤ m < p < 2, the generalized KPZ equation ut = △(um) −|∇u|p. For m = 1, we show existence and uniqueness of the so called very singular solution which is self-similar. A complete classification of self-similar solutions is also given. For m > 1, we establish the existence of very singular self-similar solution and prove that such a solution must have compact support. Moreover, we derive the interface relation. Recent experience with parallel equations where the gradient term |∇u|p is replaced by up indicates that the self-similar solutions are crucially important in study intermediate asymptotic behavior of general solutions. |
Milestones
Received: 29 September 1999
Revised: 4 September 2000
Published: 1 November 2001
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Authors |
| Yuanwei Qi | |
| Department of Mathematics Hong Kong University of Science & Technology Hong Kong |
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| Mingxin Wang | |
| Department of Applied
Mathematics Southeast University Nanjing 210018 P. R. China |
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