Dispersive waves and caustics.
Distribution near the real axis of scattering poles generated by a non-hyperbolic periodic ray
Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
We give characterizations of the distributional derivatives , , of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
Distributions and heat equation in
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Dual dynamic approach to shape optimization
Effective computation of restoring force vector in finite element method
We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...
Eigenfunction Expansions and the Pinksy Phenomenon on Compact Manifolds.
Ein nichtlinearer Interpolationssatz und seine Anwendung auf nichtlineare Wellengleichungen.
Einige Eigenschaften der Lösung der Wellengleichung mit der Korrektion von Rayleigh
Elastic wave equation
The goal of this talk is to describe the Lamé operator which drives the propagation of linear elastic waves. The main motivation for me is the work I have done in collaboration with Michel Campillo’s group from LGIT (Grenoble) on passive imaging in seismology. From this work, several mathematical problems emerged: equipartition of energy between and waves, high frequency description of surface waves in a stratified medium and related inverse spectral problems.We discuss the following topics:What...
Elastic wave propagation in parallel: the Huygens' approach.
The use of parallel computers makes it feasible to simulate elastic waves throughout large heterogeneous structures, and new domain decomposition methods can be used to increase their efficiency and decrease the computing time spent in the simulation. In this paper we introduce a simple parallel algorithm for the propagation of elastic waves in complex heterogeneous media after a finite element discretization. This method performs more efficiently than classic domain decomposition techniques based...
Encore sur les équations hyperboliques avec petit paramètre dans les espaces de Banach généraux
Energy Convergence Results for Strongly Damped Nonlinear Wave Equations.
Energy decay for solutions to semilinear systems of elastic waves in exterior domains.
Energy decay for wave equations of -Laplacian type with weakly nonlinear dissipation.
Energy decay of solutions of a wave equation of -Laplacian type with a weakly nonlinear dissipation.
Energy estimate for wave equations with coefficients in some Besov type class.
Engergy decay for the quasilinear wave equation with viscosity.
Enlarged Asymptotic Compensation in Discrete Distributed Systems
This work concerns an enlarged analysis of the problem of asymptotic compensation for a class of discrete linear distributed systems. We study the possibility of asymptotic compensation of a disturbance by bringing asymptotically the observation in a given tolerance zone 𝒞. Under convenient hypothesis, we show the existence and the unicity of the optimal control ensuring this compensation and we give its characterization