A blow-up result for a viscoelastic system in .
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Kafini, Mohammad, Messaoudi, Salim A. (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Louis Tebou (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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 another Carleman...
Louis Tebou (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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 another Carleman...
Ashyralyev, A., Sobolevskii, P.E. (2001)
Abstract and Applied Analysis
Hart F. Smith (1998)
Annales de l'institut Fourier
In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions and .
Milena Petrini (1995)
Rendiconti del Seminario Matematico della Università di Padova
Fausto Segala (1988)
Rendiconti del Seminario Matematico della Università di Padova
Colombini, Ferruccio, Rauch, Jeffrey (2008)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.The problem studied here was suggested to us by V. Petkov. Since the beginning of our careers, we have benefitted from his insights in partial differential equations and mathematical physics. In his writings and many discussions, the conjuction of deep analysis and specially interesting problems has been a source inspiration for us.The research of J. Rauch is partially supported by the U.S. National Science Foundation under grant NSF-DMS-0104096...
Glushkova, D.I., Romanov, V.G. (2003)
Sibirskij Matematicheskij Zhurnal
Romanov, V.G. (2005)
Sibirskij Matematicheskij Zhurnal
Jianmin Gao (1990)
Monatshefte für Mathematik
Reissig, M., Yagdjian, K. (2000)
Rendiconti del Seminario Matematico
Arosio, Alberto (1982)
Portugaliae mathematica
Valery Yakhno, Ali Sevimlican (2011)
Applications of Mathematics
The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem...
Michael Dreher (2003)
Banach Center Publications
Konrad Gröger (1976)
Commentationes Mathematicae Universitatis Carolinae
Rodolfo Bermejo (1991/1992)
Numerische Mathematik
Byszewski, Ludwik, Papageorgiou, Nikolaos S. (1999)
Journal of Applied Mathematics and Stochastic Analysis
Omel'yanov, Georgii A., Segundo-Caballero, Israel (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
William C. Lydord (1976)
Mathematische Annalen
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