Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations - Sorbonne Université Access content directly
Preprints, Working Papers, ... Year : 2013

Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations

Marina Ghisi
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  • PersonId : 942729
Massimo Gobbino
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Alain Haraux
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  • PersonId : 836471

Abstract

We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as t → +∞, at least as fast as a suitable negative power of t. Moreover, we prove that this decay rate is optimal in the sense that there exists a nonempty open set of initial data for which the corresponding solutions decay exactly as that negative power of t. Our results are stated and proved in an abstract Hilbert space setting, and then applied to partial differential equations.
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Dates and versions

hal-00835786 , version 1 (19-06-2013)

Identifiers

  • HAL Id : hal-00835786 , version 1

Cite

Marina Ghisi, Massimo Gobbino, Alain Haraux. Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations. 2013. ⟨hal-00835786⟩
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