On the Estimates of the Convergence Rate of the Finite Difference Schemes for the Approximation of Solutions of Hyperbolic Problems, II Part
On the existence of the wave operators for a class of nonlinear Schrödinger equations
On the -decay and local energy decay of solutions to nonlinear Klein-Gordon equations
On the poles of the scattering matrix for two convex obstacles
On the problem of determining the structure of a layered medium and the shape of an impulse source.
On the quenching of solutions of the wave equation with a nonlinear boundary condition.
On the singularities of 3-D Protter's problem for the wave equation.
On the stability of the Dirichlet problem for the vibrating string equation
On the Stabilization of the Wave Equation by the Boundary
* Partially supported by CNPq (Brazil)We study the distribution of the (complex) eigenvalues for interior boundary value problems with dissipative boundary conditions in the case of C 1 -smooth boundary under some natural assumption on the behaviour of the geodesics. As a consequence we obtain energy decay estimates of the solutions of the corresponding wave equation.
On the wave equation in curved spacetime
On the Wave Equation on a Compact Riemannian Manifold withour Conjugate Points.
On time optimal control of the wave equation, its regularization and optimality system
An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...
Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation
The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function , as terminal time . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator , as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate...
Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients
This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore,...
Optimal control systems by time-dependent coefficients using CAS wavelets.
Optimal grids for anisotropic problems.
Optimal internal dissipation of a damped wave equation using a topological approach
We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection...
Oscillating Multipliers for some Eigenfunction Expansions.
Oscillations of anharmonic Fourier series and the wave equation.
In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of⎧ utt + (-1)m Δmu = 0 (t,x) ∈ R x Ω⎨⎩ u|Γ = ... = Δm-1 u|Γ = 0 t ∈ R.These results rely on the study of a sign of almost periodic functions of a special form restricted to a bounded interval J.