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Displaying 201 – 220 of 364

On a semilinear variational problem

Bernd Schmidt (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We provide a detailed analysis of the minimizers of the functional $u \mapsto \int_{ℝ^{n}} {| \nabla u |}^{2} + D \int_{ℝ^{n}} {| u |}^{γ}$ , $γ \in (0, 2)$ , subject to the constraint ${∥ u ∥}_{L^{2}} = 1$ . This problem, e.g., describes the long-time behavior of the parabolic Anderson in probability theory or ground state solutions of a nonlinear Schrödinger equation. While existence can be proved with standard methods, we show that the usual uniqueness results obtained with PDE-methods can be considerably simplified by additional variational arguments. In addition, we investigate qualitative properties...

On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation.

Zhidkov, Peter E. (2001)

International Journal of Mathematics and Mathematical Sciences

On annealed elliptic Green's function estimates

Daniel Marahrens, Felix Otto (2015)

Mathematica Bohemica

We consider a random, uniformly elliptic coefficient field $a$ on the lattice $ℤ^{d}$ . The distribution $〈 \cdot 〉$ of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed derivative of the parabolic Green’s function $G (t, x, y)$ satisfy optimal annealed estimates which are $L^{2}$ and $L^{1}$ , respectively, in probability, i.e., they obtained bounds on $〈 | \nabla_{x} G (t, x, y) {|^{2} 〉}^{1 / 2}$ and $〈 | \nabla_{x} \nabla_{y} G (t, x, y) | 〉$ . In particular, the elliptic Green’s function $G (x, y)$ satisfies optimal annealed bounds. In their recent work, the authors...

On asymptotic stability in energy space of ground states of NLS in 2D

Scipio Cuccagna, Mirko Tarulli (2009)

Annales de l'I.H.P. Analyse non linéaire

On asymptotic stability of solitary waves for nonlinear Schrödinger equations

Vladimir S. Buslaev, Catherine Sulem (2003)

Annales de l'I.H.P. Analyse non linéaire

On coupled Klein-Gordon-Schrödinger equations with acoustic boundary conditions.

Ha, Tae Gab, Park, Jong Yeoul (2010)

Boundary Value Problems [electronic only]

On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.

G.D. Akrivis, V.A. Dougalis, ... (1991)

Numerische Mathematik

On invariant measures for some infinite-dimensional dynamical systems

P. E. Zhidkov (1995)

Annales de l'I.H.P. Physique théorique

On multi-lump solutions to the non-linear Schrödinger equation.

Magnus, Robert (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On multiply connected mesoscopic superconducting structures

Jacob Rubinstein, Michelle Schatzman (1996/1997)

Séminaire de théorie spectrale et géométrie

On nonlinear dispersive equations.

Ponce, Gustavo (1998)

Documenta Mathematica

On nonlinear Schrödinger equations

Jean Bourgain (1998)

Publications Mathématiques de l'IHÉS

On nonlinear Schrödinger equations in exterior domains

N Burq, P Gérard, N Tzvetkov (2004)

Annales de l'I.H.P. Analyse non linéaire

On perturbative cubic nonlinear Schrödinger equations under complex nonhomogeneities and complex initial conditions.

El-Tawil, Magdy A., El-Hazmy, Maha A. (2009)

Differential Equations & Nonlinear Mechanics

On Picard-Fuchs type equations related to integrable Hamiltonian systems.

Prykarpatsky, Anatoliy K., Taneri, Ufuk, Samoylenko, Valeriy (2001)

Applied Mathematics E-Notes [electronic only]

On Schrödinger maps from $T^{1}$ to $S^{2}$

Robert L. Jerrard, Didier Smets (2012)

Annales scientifiques de l'École Normale Supérieure

We prove an estimate for the difference of two solutions of the Schrödinger map equation for maps from $T^{1}$ to $S^{2} .$ This estimate yields some continuity properties of the flow map for the topology of $L^{2} (T^{1}, S^{2})$ , provided one takes its quotient by the continuous group action of $T^{1}$ given by translations. We also prove that without taking this quotient, for any $t > 0$ the flow map at time $t$ is discontinuous as a map from $𝒞^{\infty} (T^{1}, S^{2})$ , equipped with the weak topology of $H^{1 / 2},$ to the space of distributions ${(𝒞^{\infty} (T^{1}, ℝ^{3}))}^{*} .$ The argument relies in an essential...

Currently displaying 201 – 220 of 364

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Displaying 201 – 220 of 364

On a semilinear variational problem

On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation.

On annealed elliptic Green's function estimates

On asymptotic stability in energy space of ground states of NLS in 2D

On asymptotic stability of solitary waves for nonlinear Schrödinger equations

On coupled Klein-Gordon-Schrödinger equations with acoustic boundary conditions.

On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.

On invariant measures for some infinite-dimensional dynamical systems

On multi-lump solutions to the non-linear Schrödinger equation.

On multiply connected mesoscopic superconducting structures

On nonlinear dispersive equations.

On nonlinear Schrödinger equations

On nonlinear Schrödinger equations in exterior domains

On perturbative cubic nonlinear Schrödinger equations under complex nonhomogeneities and complex initial conditions.

On Picard-Fuchs type equations related to integrable Hamiltonian systems.

On Schrödinger maps from $T^{1}$ to $S^{2}$

On some Schroedinger-type variational inequalities

On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation.

On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials

On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D

Currently displaying 201 – 220 of 364