Global existence, large time behavior and life span of solutions of a semilinear parabolic cauchy problem

Tzong Yow Lee, Wei Ming Ni

Research output: Contribution to journalArticlepeer-review

161 Scopus citations

Abstract

We investigate the behavior of the solution u(x, t) of (equation formula) is the Laplace operator, p > 1 is a constant, T > 0, and φ is a nonnegative bounded continuous function in ℝn. The main results are for the case when the initial value φ has polynomial decay near x = ∞. Assuming φ φ λ(l + |x|) n with λ, a > 0, various questions of global (in time) existence and nonexistence, arge time behavior or life span of the solution u(x, i) are answered in terms of simple conditions on X, a, p and the space dimension n.

Original languageEnglish (US)
Pages (from-to)365-378
Number of pages14
JournalTransactions of the American Mathematical Society
Volume333
Issue number1
DOIs
StatePublished - Sep 1992

Keywords

  • Global existence
  • Large time asymptotic behaviors
  • Life span
  • Semilinear parabolic Cauchy problem

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