A blow-up result for a viscoelastic system in .
A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
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...
A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
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...
A note on the difference schemes for hyperbolic equations.
A parametrix construction for wave equations with coefficients
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 .
A result on the well posedness of the Cauchy problem for a class of hyperbolic operators with double characteristics
A simple construction of a parametrix for a regular hyperbolic operator
A Simple Example of Localized Parametric Resonance for the Wave Equation
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...
A stability estimate for a solution to the problem of determination of two coefficients of a hyperbolic equation.
A stability estimate for a solution to the wave equation with the Cauchy data on a timelike cylindrical surface.
A THeorem of Global Existence of Solutions to Nonlinear Wave Equations in Four Space Dimensions.
About the influence of oscillations on Strichartz-type decay estimates.
Abstract linear hyperbolic equations and asymptotic equivalence as
An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media
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...
An application of the theory of edge Sobolev spaces to weakly hyperbolic operators
An iteration method for nonlinear second order evolution equations
Analysis of an algorithm for the Galerkin-characteristic method.
Application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem.
Asymptotic and numerical description of the kink/antikink interaction.
Asymptotic Energy Propagation and Scattering of Waves in Waveguides with Cylinders.