Das Verhalten der Ableitungen globaler Lösungen nicht-linearer Wellengleichungen für grosse Zeiten.
Decay of solutions of a degenerate hyperbolic equation.
Decay rates of Volterra equations on ℝN
This note is concerned with the linear Volterra equation of hyperbolic type on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.
Dispersive estimates for a linear wave equation with electromagnetic potential.
Dispersive Estimates of Solutions to the Wave Equation with a Potential in Dimensions Two and Three
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.We prove dispersive estimates for solutions to the wave equation with a real-valued potential V.
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...
Energy decay for solutions to semilinear systems of elastic waves in exterior domains.
Équation des ondes semi-linéaires II. Contrôle des singularités et caustiques non-linéaires
Equations des ondes semi-linéaires. II. Contrôle des singularités et caustiques non linéaires.
Exact internal controllability of the elasticity system.
Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
We consider the damped semilinear viscoelastic wave equation with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms
We consider the existence, both locally and globally in time, the decay and the blow up of the solution for the extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution by Banach contraction mapping principle. The decay estimates of the solution are proved by using Nakao’s inequality. Moreover, under suitable conditions on the initial datum, we prove that the solution blow up in finite time.
Existence of global solution of a nonlinear wave equation with short-range potential
Existence of Global Solutions to Supercritical Semilinear Wave Equations
∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was studied by F. John in [13],...
Existence of solutions for discontinuous hyperbolic partial differential equations in Banach algebras.
Existence of solutions of the Darboux problem for partial differential equations in Banach spaces
Existence of weak solutions for abstract hyperbolic-parabolic equations.
Explosion de solutions classiques d’équations d’ondes quasi-linéaires en deux dimensions d’espace
Extrapolation pour les mesures de Carleson et conjecture de Kato
Finite difference approximations for partial differential equations with rapidly oscillating coefficients