TY - GEN

T1 - Upper bound estimates for local in time solutions to the semilinear heat equation on stratified lie groups in the sub-Fujita case

AU - Georgiev, Vladimir

AU - Palmieri, Alessandro

N1 - Funding Information:
Both authors acknowledge Valentino Magnani (University of Pisa) for useful discussions and support during the preparation of this work. V. Georgiev is supported in part by GNAMPA - Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project “Dinamica di equazioni nonlineari dispersive”, “Fondazione di Sardegna”, 2016. A. Palmieri is supported by the University of Pisa, Project PRA 2018 49.

PY - 2019/10/2

Y1 - 2019/10/2

N2 - 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.

AB - 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.

KW - Critical exponent of Fujita-type

KW - Lifespan estimates

KW - Semilinear heat equation

KW - Stratified Lie group

KW - Test function method

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U2 - 10.1063/1.5127465

DO - 10.1063/1.5127465

M3 - Conference contribution

AN - SCOPUS:85074371664

T3 - AIP Conference Proceedings

BT - 6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019

A2 - Slavova, Angela

PB - American Institute of Physics Inc.

T2 - 6th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2019

Y2 - 1 July 2019 through 4 July 2019

ER -