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

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

Palmieri A.
2020-01-01

Abstract

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
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/387803
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