Blow-up Estimates of the Positive Solution of a Parabolic System

Michael Pedersen, Lin Zhigui

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    This paper establishes the blow-up estimates for the systems u(t) - Deltau = 0, v(t) - Deltav = 0 in B-R x (0, T), B-R subset of R-n, with the nonlinear boundary conditions partial derivativeu/partial derivativen = u(m1)v(n1) and partial derivativev/partial derivativen = u(m2)v(n2) on S-R x (0, T) where 0 less than or equal to m(1) < 1 + m(2) and 0 <less than or equal to> n(2) < 1 + n(1). We prove that c(T - t)(-<alpha>/2) less than or equal to max u(x, t) less than or equal to C(T - t)(-alpha /2) and c(T - t)(-beta /2) less than or equal to max v(x, t) less than or equal to C(T - t)(-beta /2) under some monotonicity assumptions on the initial values, where alpha = (n(1) - n(2) + 1)/gamma, beta = (m(2) - m(1) + 1)/gamma, and gamma = (C) 2001 Academic Press.
    Original languageEnglish
    JournalJournal of Mathematical Analysis and Applications
    Volume255
    Issue number2
    Pages (from-to)551-563
    ISSN0022-247X
    DOIs
    Publication statusPublished - 15 Mar 2001

    Keywords

    • nonlinear boundary
    • blow-up rate

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