On the strongly damped wave equation with nonlinear damping and source terms.
On the structure of layers for singularly perturbed equations in the case of unbounded energy
We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating...
On the structure of layers for singularly perturbed equations in the case of unbounded energy
We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...
On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation
2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator. As an illustration of...
On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization
We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give some numerical...
On the viscous Burgers equation in unbounded domain.
On the wave equations in the spacetime of a cosmic string
On the wave equations with memory in noncylindrical domains.
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On the Yang-Mills heat equation in two and three dimensions.
On the -convergence of Laplace-Beltrami operators in the plane.
On uniqueness and stability of steady-state carrier distributions in semiconductors
Ondes oscillantes semi-linéaires en 1.d
Optimal energy decay rate of coupled wave equations.
Optimization problems for structural acoustic models with thermoelasticity and smart materials
Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...
Optique géométrique oscillante en présence d'un grand choc
Orbital stability for polytropic galaxies
Oscillations of a nonlinearly damped extensible beam
It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times.
Otto Vejvoda passed away
Parabolic boundary-value problems with equivalued surface on the domain with a thin layer.