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Indexed by:期刊论文

Date of Publication:2014-07-01

Journal:DIFFERENTIAL AND INTEGRAL EQUATIONS

Included Journals:SCIE

Volume:27

Issue:7-8

Page Number:643-658

ISSN No.:0893-4983

Abstract:This paper studies the evolution p-Laplacian equation with inner absorption u(t) = (vertical bar u(x)vertical bar(P-2)u(x))(x) - lambda u(k) in R+ x R+ subject to nonlinear boundary flux vertical bar u(x vertical bar)(P-2)u(x)(0, t) = u(q) (0, t). First, we determine the critical boundary flux exponent q* = max{2(p-1)/p, (k+1)(P-1)/p} to identify global and nonglobal solutions, relying on or independent of initial data. It is interesting to find that, for the critical case q = q* (the balanced case between inner absorption and boundary flux) with the absorption coefficient lambda > 0 small, there is the so-called critical Fajita absorption exponent k(c)= 2p - 1 > k(0) = 1 related to a Fajita type conclusion that (i) when k <= k(c), all solutions are global; (ii) if no <r < ice, the solutions blow up in finite time under any nontrivial nonnegative initial data; (iii) if n > nc, there are both global and nonglobal solutions, respectively, determined by the sizes of initial data. Obviously, when lambda > 0 large for the balanced case q = q*, the absorption would overcome the boundary flux to yield global solutions. Furthermore, we will show how and in what ways the inner absorption affects the evolution of the support of solutions, where a complete classification for all the nonlinear parameters is given to distinguish localization and non-localization behavior of the global solutions.