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Indexed by:期刊论文

Date of Publication:2014-08-15

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、Scopus

Volume:416

Issue:2

Page Number:710-723

ISSN No.:0022-247X

Key Words:p-Laplacian; Convection; Localization; Shrinking; Expanding

Abstract: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.