Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m
SAK principle for a class of Grushin-type operators.
We prove Fefferman's SAK Principle for a class of hypoelliptic operators on R2 whose nonnegative symbol vanishes anisotropically on the characteristic manifold.
Scalar boundary value problems on junctions of thin rods and plates
We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, i.e. the relative...
Scaling limits and regularity results for a class of Ginzburg-Landau systems
Scalings in homogenisation of reaction, diffusion and interfacial exchange in a two-phase medium
Scattering amplitude for the Schrödinger equation with strong magnetic field
In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.
Scattering for 1D cubic NLS and singular vortex dynamics
We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions form a family of evolving regular curves in that develop a singularity in finite time, indexed by a parameter . We consider curves that are small regular perturbations of for a fixed time . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of local existence...
Scattering for Semilinear Wave Equations with Small Data in Three Space Dimensions.
Scattering of small solutions of a symmetric regularized-long-wave equation
We study the decay in time of solutions of a symmetric regularized-long-wave equation and we show that under some restriction on the form of nonlinearity, the solutions of the nonlinear equation have the same long time behavior as those of the linear equation. This behavior allows us to establish a nonlinear scattering result for small perturbations.
Scattering theory for a nonlinear system of wave equations with critical growth
We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure ⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u, ⎨ ⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v, for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for the potential...
Scattering theory for Hartree type equations
Scattering theory for one-dimensional step potentials
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
Schrödinger equations with unique positive isolated singularities.
Schrödinger-Poisson equations with supercritical growth.
Schrödingers Operators with Singular Magnetic Vector Potentials.
Second order evolution equations with parameter
We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.
Second order nonpersistence of the sine Gordon breather under an exceptional perturbation
Second order parabolic systems, optimal regularity, and singular sets of solutions
Second order quasilinear functional evolution equations
We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in (boundedness and stabilization as ) are shown.