Smoothness effect and decay on a class of non linear evolution equation
Jaime E. Muñoz Rivera (1992)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Jaime E. Muñoz Rivera (1992)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Gustavo Perla Menzala (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Belhassen Dehman, Gilles Lebeau, Enrique Zuazua (2003)
Annales scientifiques de l'École Normale Supérieure
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Renato Manfrin (1994)
Rendiconti del Seminario Matematico della Università di Padova
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J.-L. Joly, G. Métivier, J. Rauch (1995)
Annales scientifiques de l'École Normale Supérieure
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Mitsuru Ikawa (1988)
Annales de l'institut Fourier
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We study the decay of solutions to the wave equation in the exterior of several strictly convex bodies. A sufficient condition for exponential decay of the local energy is expressed in terms of the period and the Poincare map of periodic rays in the exterior domain.
Catalano, Fabio (1999)
Serdica Mathematical Journal
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∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...” In this work we analyse the nonlinear Cauchy problem (∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ), whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1, x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can be considerated a pertubation of the case when the quadratic term has constant coefficient...