Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity

Vladimir Georgiev, Alessandro Palmieri

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the Cauchy problem for the semilinear damped wave equation on the Heisenberg group with power non-linearity. We prove that the critical exponent is the Fujita exponent pFuj(Q) = 1+2/Q, where Q is the homogeneous dimension of the Heisenberg group.

On the one hand, we will prove the global existence of small data solutions for p > pFuj(Q) in an exponential weighted energy space. On the other hand, a blow-up result for 1 < p ≤ pFuj(Q) under certain integral sign assumptions for the Cauchy data by using the test function method.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Aug 8

Keywords

  • Critical exponent
  • Damped wave equation
  • Energy spaces with exponential weight
  • Heisenberg group
  • Test function method

ASJC Scopus subject areas

  • General

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