On the stabilization of wave-advection coupling. (Sur la stabilisation d'un couplage ondes-advection.)
On the stationary solutions of Burgers' equation
On the Stefan problem: the variational approach and some applications
On the Stefan problem with a small parameter
We consider the multidimensional two-phase Stefan problem with a small parameter κ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to κ) estimate of the solution of the Stefan problem for t ≤ T₀, T₀ independent of κ, and the existence and estimate of the solution of the Florin problem (Stefan problem with κ = 0) in Hölder spaces.
On the Stokes and Navier-Stokes flows in a perturbed half-space
We give the estimate for the Stokes semigroup in a perturbed half-space and some global in time existence theorems for small solutions to the Navier-Stokes equation.
On the strong solution for the 3D stochastic Leray- model.
On the strong unique continuation prinicple for inequalities of Maxwell type.
On the strongly damped wave equation and the heat equation with mixed boundary conditions.
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 structure of solutions to elliptic problems with strong anisotropy.
On the structure of spectra of travelling waves.
On the structure of the conformal Gaussian curvature equation on R2. II.
On the time periodic free boundary associated to some nonlinear parabolic equations.
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 two-phase membrane problem with coefficients below the Lipschitz threshold
On the uniform boundedness of the solutions of systems of reaction-diffusion equations.
On the uniformly continuity of the solution map for two dimensional wave maps.
On the unique continuation property for a nonlinear dispersive system.