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¯.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/374640
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