In this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity | u| p or nonlinearity of derivative type | ut| p, in any space dimension n⩾ 1 , for supercritical powers p> p¯. The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive Lr- Lq long time decay estimates for the solution in the full range 1 ⩽ r⩽ q⩽ ∞. The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers p< p¯.
Global small data solutions for semilinear waves with two dissipative terms
D'Abbicco M.;Girardi G.
2022-01-01
Abstract
In this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity | u| p or nonlinearity of derivative type | ut| p, in any space dimension n⩾ 1 , for supercritical powers p> p¯. The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive Lr- Lq long time decay estimates for the solution in the full range 1 ⩽ r⩽ q⩽ ∞. The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers p< p¯.File 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.
