Apparition éventuelle de singularités dans des problèmes d'évolution non linéaires
Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept
Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...
Application of Moser's method to a certain type of evolution equations
Application of restricted Backlund transformation to linearization of second order nonlinear parabolic equation
Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation.
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 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 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 symmetry methods to the theory of plasma physics.
Applications of the new compound Riccati equations rational expansion method and Fan's subequation method for the Davey-Stewartson equations.
Approximate ad hoc parametric solutions for nonlinear first-order PDEs governing two-dimensional steady vector fields.
Approximate controllability for a system of Schrödinger equations modeling a single trapped ion
Approximate controllability of a hydro-elastic coupled system
Approximate controllability of a hydro-elastic coupled system
We analyze the controllability of the motion of a fluid by means of the action of a vibrating shell coupled at the boundary of the fluid. The model considered is linear. We study its approximate controllability, i.e. whether the fluid may reach a dense set of final configurations at a given time. We show that this problem can be reduced to a unique continuation question for the Stokes system. We prove that this unique continuation property holds generically among analytic domains and therefore,...
Approximate controllability of a reaction-diffusion system with a cross-diffusion matrix and fractional derivatives on bounded domains.
Approximate method for studying the waves propagating along the interface between air-water.
Approximate solution of the nonlinear heat conduction equation in a semi-infinite domain.
Approximate solutions of the incompressible Euler equations with no concentrations
Approximate traveling wave solutions of coupled Whitham-Broer-Kaup shallow water equations by homotopy analysis method.