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

Vladimir Georgiev, Alessandro Palmieri

研究成果: Article

抜粋

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.

元の言語English
ページ(範囲)420-448
ページ数29
ジャーナルJournal of Differential Equations
269
発行部数1
DOI
出版物ステータスPublished - 2020 6 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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