Initial value problems in elasticity
Rolf Leis (1992)
Banach Center Publications
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Rolf Leis (1992)
Banach Center Publications
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Cabanillas Lapa, E., Huaringa Segura, Z., Leon Barboza, F. (2005)
Journal of Applied Mathematics
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Jean-François Bony, Vesselin Petkov (2005-2006)
Séminaire Équations aux dérivées partielles
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Kian, Yavar (2010)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 35B40, 35L15. We obtain local energy decay as well as global Strichartz estimates for the solutions u of the wave equation ∂t2 u-divx(a(t,x)∇xu) = 0, t ∈ R, x ∈ Rn, with time-periodic non-trapping metric a(t,x) equal to 1 outside a compact set with respect to x. We suppose that the cut-off resolvent Rχ(θ) = χ(U(T, 0)− e−iθ)−1χ, where U(T, 0) is the monodromy operator and T the period of a(t,x), admits an holomorphic continuation to...
Paolo Secchi (2002)
Rendiconti del Seminario Matematico della Università di Padova
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Louis Tebou (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt. 46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on...