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

研究成果: Conference contribution

1 引用 (Scopus)

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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.

元の言語English
ホスト出版物のタイトル6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019
編集者Angela Slavova
出版者American Institute of Physics Inc.
ISBN(電子版)9780735419049
DOI
出版物ステータスPublished - 2019 10 2
イベント6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019 - St. Constantine and Helena, Bulgaria
継続期間: 2019 7 12019 7 4

出版物シリーズ

名前AIP Conference Proceedings
2159
ISSN(印刷物)0094-243X
ISSN(電子版)1551-7616

Conference

Conference6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019
Bulgaria
St. Constantine and Helena
期間19/7/119/7/4

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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  • これを引用

    Georgiev, V., & Palmieri, A. (2019). Upper bound estimates for local in time solutions to the semilinear heat equation on stratified lie groups in the sub-Fujita case. : A. Slavova (版), 6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019 [020003] (AIP Conference Proceedings; 巻数 2159). American Institute of Physics Inc.. https://doi.org/10.1063/1.5127465