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.
Publisher Copyright:
© 2019 Author(s).
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 -