Evolution systems for paraxial wave equations of Schrödinger-type with non-smooth coefficients

DOI10.1016/j.jde.2008.06.022zbMath1173.35108arXivmath/0506410OpenAlexW2155171008MaRDI QIDQ944302

Michael Oberguggenberger, Günther Hörmann, Maarten V. de Hoop

Publication date: 16 September 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506410

zbMATH Keywords

distribution spaces with mixed regularitylack of lateral regularitystrongly continuous evolution systems

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Initial value problems for linear higher-order PDEs (35G10) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items

White-Noise Paraxial Approximation for a General Random Hyperbolic System, The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data, Limits of regularizations for generalized function solutions to the Schrödinger equation with `square root of delta' initial value, Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients, Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data, On the wave equation with multiplicities and space-dependent irregular coefficients

Cites Work

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• Seismic inverse scattering in the downward continuation approach
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Semigroups of linear operators and applications to partial differential equations
• Lectures on nonlinear hyperbolic differential equations
• A comparison of parabolic wave theories for linearly elastic solids
• Hyperbolic operators with non-Lipschitz ceofficients
• A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media
• Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile
• A Multi-Scale Approach to Hyperbolic Evolution Equations with Limited Smoothness
• Reflection of singularities of solutions to systems of differential equations
• Well-Posedness of One-Way Wave Equations and Absorbing Boundary Conditions
• Microlocal analysis of seismic inverse scattering in anisotropic elastic media
• SELF-AVERAGING IN TIME REVERSAL FOR THE PARABOLIC WAVE EQUATION
• Statistical Stability in Time Reversal
• Modeling of Seismic Data in the Downward Continuation Approach