Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems

Hendrik J. Kuiper

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We consider the problem (formula presented) with nonnegative, nontrivial, continuous initial condition, (formula presented) An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p ≤ pc. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu0(x), σ > 0, by obtaining a bound of the form T ≤ C0σ.

Original languageEnglish (US)
Pages (from-to)1-11
Number of pages11
JournalElectronic Journal of Differential Equations
Volume2003
StatePublished - Jun 13 2003

Fingerprint

Nonnegative Solution
Life Span
Integral Inequality
Parabolic Problems
Cauchy Problem
Global Solution
Initial conditions
Non-negative
Exponent
Estimate
Form

Keywords

  • Blow-up
  • Critical exponent
  • Lifespan
  • Nonlinear parabolic equation

ASJC Scopus subject areas

  • Analysis

Cite this

Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems. / Kuiper, Hendrik J.

In: Electronic Journal of Differential Equations, Vol. 2003, 13.06.2003, p. 1-11.

Research output: Contribution to journalArticle

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