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 $p_{Fuj}(mathcal{Q}) = 1+2/mathcal{Q}$, where $mathcal{Q}$ is the homogeneous dimension of the Heisenberg group. On the one hand, we will prove the global existence of small data solutions for $p>p_{Fuj}(mathcal{Q})$ 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
Gueorguiev, Vladimir Simeonov;Palmieri, Alessandro
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 $p_{Fuj}(mathcal{Q}) = 1+2/mathcal{Q}$, where $mathcal{Q}$ is the homogeneous dimension of the Heisenberg group. On the one hand, we will prove the global existence of small data solutions for $p>p_{Fuj}(mathcal{Q})$ in an exponential weighted energy space. On the other hand, a blow-up result for $1File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
