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论文类型：期刊论文

发表时间：2014-07-01

发表刊物：DIFFERENTIAL AND INTEGRAL EQUATIONS

收录刊物：SCIE

卷号：27

期号：7-8

页面范围：643-658

ISSN号：0893-4983

摘要：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.