Construction of type i blowup solutions for a higher order semilinear parabolic equation

Tej Eddine Ghoul, Tien Van Nguyen, Hatem Zaag

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the higher-order semilinear parabolic equation αtu=-(-Δ)mu+u|u|p-1, in the whole space ℝN, where p > 1 and m ≥ 1 is an odd integer. We exhibit type I non self-similar blowup solutions for this equation and obtain a sharp description of its asymptotic behavior. The method of construction relies on the spectral analysis of a non self-adjoint linearized operator in an appropriate scaled variables setting. In view of known spectral and sectorial properties of the linearized operator obtained by Galaktionov [15], we revisit the technique developed by Merle-Zaag [23] for the classical case m = 1, which consists in two steps: the reduction of the problem to a finite dimensional one, then solving the finite dimensional problem by a classical topological argument based on the index theory. Our analysis provides a rigorous justification of a formal result in [15].

Original languageEnglish (US)
Pages (from-to)388-412
Number of pages25
JournalAdvances in Nonlinear Analysis
Volume9
Issue number1
DOIs
StatePublished - Mar 1 2019

Keywords

  • Blowup profile
  • Blowup solution
  • Higher order parabolic equation
  • Stability

ASJC Scopus subject areas

  • Analysis

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