Application of Moser's method to a certain type of evolution equations
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Application of the approximate analytic prolongment to the boundary problems of the partial differential equations
Application of very weak formulation on homogenization of boundary value problems in porous media
The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard energy method or the method of two-scale convergence, this approach is not based on the weak formulation of the problem but on the very weak formulation. To illustrate the method and its advantages we treat the stationary, incompressible Navier-Stokes system with the non-homogeneous Dirichlet boundary condition in periodic porous medium. The...
Applications bilinéaires compatibles avec un opérateur hyperbolique
Applications of a weighted symmetrization inequality to elastic membranes and plates.
Applications of an extended -expansion method to find exact solutions of nonlinear PDEs in mathematical physics.
Applications of geometric measure theory to the study of Gauss- Weierstrass and Poisson integrals.
Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences
Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized...
Applications of the bifurcation theory to evaluating critical conditions of the thermal explosion
Applications of the new compound Riccati equations rational expansion method and Fan's subequation method for the Davey-Stewartson equations.
Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires
On s’intéresse à des systèmes symétriques hyperboliques multidimensionnels en présence d’une semilinéarité. Il est bien connu que ces systèmes admettent des solutions discontinues, régulières de part et d’autre d’une hypersurface lisse caractéristique de multiplicité constante. Une telle solution étant donnée, on montre que est limite quand de solutions du système perturbé par une viscosité de taille . La preuve utilise un problème mixte parabolique et des développements de couches limites....
Approximate controllability for a linear model of fluid structure interaction
Approximate controllability for a linear model of fluid structure interaction
We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular,...
Approximate controllability of linear parabolic equations in perforated domains
In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are -periodic and of size . We show that, as , the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion...
Approximate Controllability of linear parabolic equations in perforated domains
In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are ε-periodic and of size ε. We show that, as ε → 0, the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion...
Approximate inertial manifolds for nonlinear parabolic equations via steady-state determining mapping.
Approximation de la solution de viscosité d'un problème d'Hamilton-Jacobi.
Approximation des systèmes d'opérateurs pseudodifférentiels
Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method
The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...