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论文类型：期刊论文

发表时间：2009-03-15

发表刊物：NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

收录刊物：SCIE、EI、Scopus

卷号：70

期号：6

页面范围：2176-2197

ISSN号：0362-546X

关键字：Coupled heat equations; Critical exponents; Nonlinear absorption; Nonlinear boundary flux; Multiple blow-up rates; Blow-up set; Characteristic algebraic system

摘要：This paper studies heat equations with inner absorptions and coupled boundary fluxes of mixed-type nonlinearities. At first, the critical exponent is obtained, and simply described via a characteristic algebraic system introduced by us. Then, as the main results of the paper, three blow-up rates are established under different dominations of nonlinearities for the one-dimensional case, and represented in another characteristic algebraic system. In particular, it is observed that unlike those in previous literature on parabolic models with absorptions, two of the multiple blow-up rates obtained here do depend on the absorption exponents. In the known works, the absorptions affect the blow-up criteria, the blow-up time, as well as the initial data required for the blow-up of solutions, all without changing the blow-up rates. To our knowledge, this is the first example of absorption-dependent blow-up rates, exploiting the significant interactions among diffusions, inner absorptions and nonlinear boundary fluxes in the coupled system. It is also proved that the blow-up of solutions in the model occurs on the boundary only. (C) 2008 Elsevier Ltd. All fights reserved.