The Schrödinger Equation Type with a Nonelliptic Operator

DOI10.1080/03605300601128074zbMath1387.35142OpenAlexW2037418620MaRDI QIDQ3436035

Delphine Salort

Publication date: 8 May 2007

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300601128074

zbMATH Keywords

dispersionWKB methodStrichartz estimatesstationary phase methodSchrödinger equation with nonelliptic and degenerate operator

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Dispersion theory, dispersion relations arising in quantum theory (81U30)

Related Items (4)

Sharp Strichartz estimates for some variable coefficient Schrödinger operators on \(\mathbb{R}\times\mathbb{T}^2 \) ⋮ Strichartz estimates for the periodic non-elliptic Schrödinger equation ⋮ Essential self-adjointness of real principal type operators ⋮ Strichartz Estimates for Non-Elliptic Schrödinger Equations on Compact Manifolds

Cites Work

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• Degenerative dispersion laws, motion invariants and kinetic equations
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Exponential sums and nonlinear Schrödinger equations
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• Nonelliptic Schrödinger equations
• Concentration and lack of observability of waves in highly heterogeneous media
• Nonexistence of travelling wave solutions to nonelliptic nonlinear Schrödinger equations
• Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications
• Variable coefficient Schrödinger flows for ultrahyperbolic operators
• Multi-Vortex Solutions of a Two-Dimensional Nonlinear Wave Equation
• STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS
• On the initial value problem for the Davey-Stewartson systems
• Endpoint Strichartz estimates
• Dispersion and Strichartz Inequalities for Schrödinger Equations with Singular Coefficients
• A Strichartz Inequality for the Schrödinger Equation on Nontrapping Asymptotically Conic Manifolds
• On three-dimensional packets of surface waves
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Equations d'ondes quasilineaires et estimations de Strichartz

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