Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2009-03-15

Journal: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 70

Issue: 6

Page Number: 2176-2197

ISSN: 0362-546X

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

Abstract: 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.