Large-time geometrical properties of solutions of the Barenblatt equation of elasto-plastic filtration

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Huang, Yong³  Vazquez, Juan L.^1,2 

[1] Univ Autonoma Madrid, Dept Matemat, Madrid 28046, Spain

[2] Univ Autonoma Madrid, ICMAT, Madrid 28046, Spain

[3] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

关键词: Log-concavity;    Elasto-plastic filtration;    Fully nonlinear parabolic equation;   

DOI  :  10.1016/j.jde.2011.12.010

来源: Elsevier

【 摘 要 】

We study the geometric behavior for large times of the solutions of the following equation u(t) + gamma vertical bar u(t)vertical bar = Delta u, 0 < vertical bar gamma vertical bar <1, posed in the whole space R-N, for N >= 1 when the initial data are nonnegative, continuous and compactly supported. We prove that, after a finite time, log(u) becomes a concave function in the space variable and converges to all orders of differentiability to a certain parabolic shape, so-called Barenblatt-type profile, which was described in Kamin et al. (1991) [20]. Extensions to more general fully nonlinear equations are considered. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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