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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Georgiev, Vladimir^1,2,3  Palmieri, Alessandro¹ 

[1] Univ Pisa, Dept Math, Largo B Pontecorvo 5, I-56127 Pisa, Italy

[2] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

[3] BAS Acad, Inst Math & Informat, G Bonchev Str,Block 8, Sofia 1113, Bulgaria

关键词: Damped wave equation;    Heisenberg group;    Critical exponent;    Test function method;    Energy spaces with exponential weight;   

DOI  :  10.1016/j.jde.2019.12.009

来源: Elsevier

【 摘 要 】

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 p(Fuj)(Q) = 1 + 2/Q, where Qis the homogeneous dimension of the Heisenberg group. On the one hand, we will prove the global existence of small data solutions for p > p(Fuj)(Q) in an exponential weighted energy space. On the other hand, a blow-up result for 1 < p <= p(Fuj)(Q) under certain integral sign assumptions for the Cauchy data by using the test function method. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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