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论文类型：期刊论文

发表时间：2014-08-15

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE、Scopus

卷号：416

期号：2

页面范围：710-723

ISSN号：0022-247X

关键字：p-Laplacian; Convection; Localization; Shrinking; Expanding

摘要：Consider the Cauchy-Dirichlet problem in half space for a one-dimensional evolution p-Laplacian with convection for p > 2, and pay attention to the interface xi(t) = sup{x; u(x, t) > 0}. It is well known that hm(t ->+infinity) xi(t)= +infinity in the absence of the convection, while the inclusion of the first-order term may change the property of finite (or infinite) speed of propagation. In this paper, it will be shown that the nonlinear convection plays a very important role to the evolution of xi(t). For the convection with promoting diffusion, the fast propagation phenomenon occurs (i.e. u(x, t) > 0 whenever t > 0) if the convection is strong enough, otherwise, xi(t) remains finite and non-localized. While under the convection with counteracting diffusion, if the convection is strong enough, localization (even shrinking and extinction) appears, otherwise, xi(t) keeps non-localized. In addition, it is found that the time-related boundary data are significant also to the behavior of solutions: the decay or incremental rates of the boundary data affect not only the contraction or expansion of the supports, but also the propagation speed of the interface. (C) 2014 Elsevier Inc. All rights reserved.