Solutions en grand temps d'équations d'ondes non linéaires
Solutions for a hyperbolic system with boundary differential inclusion and nonlinear second-order boundary damping.
Solutions of an elliptic system with a nearly critical exponent
Solutions of Ginzburg-Landau equations and critical points of the renormalized energy
Solutions oscillantes des équations de Carleman
Solvability and asymptotics of solutions of crack-type boundary-contact problems of the ocuple-stress elasticity.
Some applications of parabolic comparison principles to the study of decay estimates.
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...
Some Gradient Estimates on Covering Manifolds
Let M be a complete Riemannian manifold which is a Galois covering, that is, M is periodic under the action of a discrete group G of isometries. Assuming that G has polynomial volume growth, we provide a new proof of Gaussian upper bounds for the gradient of the heat kernel of the Laplace operator on M. Our method also yields a control on the gradient in case G does not have polynomial growth.
Some models of Cahn-Hilliard equations in nonisotropic media
We derive in this article some models of Cahn-Hilliard equations in nonisotropic media. These models, based on constitutive equations introduced by Gurtin in [19], take the work of internal microforces and also the deformations of the material into account. We then study the existence and uniqueness of solutions and obtain the existence of finite dimensional attractors.
Some notes to certain modification of the Oseen problem
Some properties of solutions of the pseudo-parabolic equation.
Some properties of stationary parabolic mixed problems in an infinite cylinder
Some properties of two-scale convergence
We reformulate and extend G. Nguetseng’s notion of two-scale convergence by means of a variable transformation, and outline some of its properties. We approximate two-scale derivatives, and extend this convergence to spaces of differentiable functions. The two-scale limit of derivatives of bounded sequences in the Sobolev spaces , , and is then characterized. The two-scale limit behaviour of the potentials of a two-scale convergent sequence of irrotational fields is finally studied.
Some qualitative problems in the theory of second order partial differential equations
Some recent results on blow-up on the boundary for the heat equation
Some remarks on a second order evolution equation.
Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings