TY - JOUR

T1 - Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity

AU - Georgiev, Vladimir

AU - Palmieri, Alessandro

N1 - Publisher Copyright:
Copyright © 2019, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019/8/8

Y1 - 2019/8/8

N2 - 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 pFuj(Q) = 1+2/Q, where Q is the homogeneous dimension of the Heisenberg group.On the one hand, we will prove the global existence of small data solutions for p > pFuj(Q) in an exponential weighted energy space. On the other hand, a blow-up result for 1 < p ≤ pFuj(Q) under certain integral sign assumptions for the Cauchy data by using the test function method.

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

KW - Critical exponent

KW - Damped wave equation

KW - Energy spaces with exponential weight

KW - Heisenberg group

KW - Test function method

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M3 - Article

AN - SCOPUS:85094011344

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -