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Indexed by:期刊论文

Date of Publication:2008-08-01

Journal:ADVANCED NONLINEAR STUDIES

Included Journals:SCIE、Scopus

Volume:8

Issue:3

Page Number:603-617

ISSN No.:1536-1365

Key Words:double degeneracy; critical exponent; absorption; nonlinear boundary source; blow-up; global solution

Abstract:This paper deals with a doubly degenerate parabolic equation with absorption (u(n))(t) = (vertical bar u(x)vertical bar(m-1)u(x))(x) - eta u(p) in (0, 1) x (0, T) subject to the boundary source (vertical bar u(x)vertical bar(m-1)u(x))(1, t) = u(q)(1, t). The critical boundary source exponent q(c) is determined under different dominations to identify global and non-global solutions. A complete classification for all of the four nonlinear exponents m, n, p, q with the coefficient eta draws a very clear picture of interactions among the multi-nonlinearities. It is shown that q(c) depends on the absorption exponent p if and only if p > n. It is found as well that q(c) is related to small m only: q(c) relies on m if and only if m < p when p > n, also q(c) relies on m if and only if m < n when p <= n. The behavior of solutions in the critical case of q = q(c) is interesting. The absorption coefficient eta affects the critical property of solutions with q = q(c) if and only if p > n: the case q = q(c) belongs to the global existence situation (regardless of the absorption coefficient eta) if p <= n; while for q = q(c) with p > n, the solutions may be both global and non-global, depending on the size of the absorption coefficient.