The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data

DOI10.1007/s00605-010-0232-xzbMath1238.46036arXiv0909.5672OpenAlexW2050177735MaRDI QIDQ636850

Günther Hörmann

Publication date: 30 August 2011

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5672

zbMATH Keywords

Colombeau generalized functionsgeneralized solutions of differential equations

Mathematics Subject Classification ID

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Generalized solutions to partial differential equations (35D99)

Related Items (9)

Schrödinger equation with singular position dependent mass ⋮ Generalised solutions to linear and non-linear Schrödinger-type equations with point defect: Colombeau and non-Colombeau regimes ⋮ Singular solution of the Hartree equation with a delta potential ⋮ Symmetric hyperbolic systems in algebras of generalized functions and distributional limits ⋮ Limits of regularizations for generalized function solutions to the Schrödinger equation with `square root of delta' initial value ⋮ Wave Equations and Symmetric First-order Systems in Case of Low Regularity ⋮ A nonlinear theory of generalized functions ⋮ Generalized solution to multidimensional cubic Schrödinger equation with delta potential ⋮ A characterization of singular Schrödinger operators on the half-line

Cites Work

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• Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics
• Evolution systems for paraxial wave equations of Schrödinger-type with non-smooth coefficients
• Semigroups of linear operators and applications to partial differential equations
• Multiplication of distributions. A tool in mathematics, numerical engineering and theoretical physics
• A comparison of parabolic wave theories for linearly elastic solids
• Hyperbolic operators with non-Lipschitz ceofficients
• Nonlinear Schrödinger equation with singular potential and initial data
• The wave equation on singular space-times
• Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory
• Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems
• On Lorentz geometry in algebras of generalized functions
• Geodesics and geodesic deviation for impulsive gravitational waves
• The ultrarelativistic Reissner–Nordstro/m field in the Colombeau algebra
• A note on the Penrose junction conditions
• Well-Posedness of One-Way Wave Equations and Absorbing Boundary Conditions
• SELF-AVERAGING IN TIME REVERSAL FOR THE PARABOLIC WAVE EQUATION
• Generalized solutions to the cubic Schrödinger equation
• The use of generalized functions and distributions in general relativity
• PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA
• Heat equation with singular potential and singular data
• Measure and integration theory. Transl. from the German by Robert B. Burckel

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