Metadata language
Raport Badawczy = Research Report ; RB/93/2007
Creator:Lasiecka, Irena ; Toundykov, Daniel
Publisher:Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
Place of publishing: Date issued/created: Description:30 stron ; 21 cm ; Bibliografia s. 29-30
Abstract:We derive global in time a priori bounds on higher-level energy norms of strong solutions to a semilinear wave equation: in particular, we prove that despite the influence of a nonlinear source, the evolution of a smooth initial state is globally bounded in the strong topology ∼ H2 × H1. And the bound is uniform with respect to the corresponding norm of the initial data. It is known that an m-accretive semigroup generator monotonically propagates smoothness of the initial condition; however, this result does not hold in general for Lipschitz perturbations of monotone systems where higher order Sobolev norms of the solution may blowup asymptotically as t → ∞. Due to nonlinearity of the system, the only a priori global-in-time bound that follows from classical methods is that on finite energy: ∼ H1 × L2. We show that under some correlation between growth rates of the damping and the source, the norms of topological order above the finite energy level remain globally bounded. Moreover, we also establish this result when damping exhibits sublinear or superlinear growth at the origin, or at infinity, which has immediate applications to asymptotic estimates on the decay rates of the finite energy. The approach presented in the paper is not specific to the wave equation, and can be extended to other hyperbolic systems: e.g. plate, Maxwell, and Schrödinger equations.
Relation:Raport Badawczy = Research Report
Resource type: Detailed Resource Type: Source: Language: Language of abstract: Rights:Licencja Creative Commons Uznanie autorstwa 4.0
Terms of use:Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -
Digitizing institution:Instytut Badań Systemowych Polskiej Akademii Nauk
Original in:Biblioteka Instytutu Badań Systemowych PAN
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