Upper bound estimates for local in time solutions to the semilinear heat equation on stratified lie groups in the sub-Fujita case

Vladimir Georgiev, Alessandro Palmieri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

In this note, we consider the Cauchy problem for the semilinear heat equation in a homogeneous stratified group G of homogeneous dimension Q and with power nonlinearity |u|p. In this framework, the heat operator is given by ât ΔH, where ΔH is the sub-Laplacian on G We prove the nonexistence of global in time solutions for exponents in the sub-Fujita case, that is for 1 < p ≤ 1 + 2/Q, under suitable integral sign assumptions for the Cauchy data. Besides, we derive upper bound estimates for the lifespan of local in time solutions both in the subcritical case and in the critical case.

Original languageEnglish
Title of host publication6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019
EditorsAngela Slavova
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735419049
DOIs
Publication statusPublished - 2019 Oct 2
Event6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019 - St. Constantine and Helena, Bulgaria
Duration: 2019 Jul 12019 Jul 4

Publication series

NameAIP Conference Proceedings
Volume2159
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019
Country/TerritoryBulgaria
CitySt. Constantine and Helena
Period19/7/119/7/4

Keywords

  • Critical exponent of Fujita-type
  • Lifespan estimates
  • Semilinear heat equation
  • Stratified Lie group
  • Test function method

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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