Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach

DOI10.1007/s10208-014-9232-xzbMath1375.81163OpenAlexW1982368468MaRDI QIDQ895701

Enrique Zuazua, Aurora Marica

Publication date: 4 December 2015

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/237

zbMATH Keywords

finite difference approximationsnon-uniform meshesbi-characteristic raysumklapp/internal reflectionvariable coefficients transport/wave equationsWigner transform/measure

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Singularity in context of PDEs (35A21) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items

Spectral analysis of finite-dimensional approximations of \(1d\) waves in non-uniform grids ⋮ Propagation of one- and two-dimensional discrete waves under finite difference approximation ⋮ Analysis of an observer strategy for initial state reconstruction of wave-like systems in unbounded domains ⋮ Observability inequalities for Hermite bi-cubic orthogonal spline collocation methods of 2-D integro-differential equations in the square domains ⋮ Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential operators ⋮ Numerical hypocoercivity for the Kolmogorov equation ⋮ Boundary Stabilization of Numerical Approximations of the 1-D Variable Coefficients Wave Equation: A Numerical Viscosity Approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Wave propagation and reflection in irregular grids for hyperbolic equations
• Transport equation and Cauchy problem for BV vector fields
• Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes
• Ordinary differential equations, transport theory and Sobolev spaces
• Transport equations for elastic and other waves in random media
• Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
• Locally Toeplitz sequences: Spectral properties and applications
• On Wigner measures
• Analysis of preconditioning strategies for collocation linear systems
• On two-dimensional Hamiltonian transport equations with \(\mathbb L^p_{\text{loc}}\) coefficients
• The pseudo-differential approach to finite differences revisited
• Oscillations of concentration effects in semilinear dispersive wave equations
• Concentration and lack of observability of waves in highly heterogeneous media
• Weak observability estimates for 1-D wave equations with rough coefficients
• Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications
• On Liouville Transport Equation with Force Field inBV_loc
• Survey of the stability of linear finite difference equations
• Exact Controllability for Multidimensional Semilinear Hyperbolic Equations
• Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes
• Well Posedness in any Dimension for Hamiltonian Flows with NonBVForce Terms
• Group Velocity in Finite Difference Schemes
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Homogenization limits and Wigner transforms
• Escape Function Conditions for the Observation, Control, and Stabilization of the Wave Equation
• On the Quantum Correction For Thermodynamic Equilibrium
• Wigner Measures in the Discrete Setting: High-Frequency Analysis of Sampling and Reconstruction Operators
• The rate at which energy decays in a string damped at one end
• Numerical Approximation of Exact Controls for Waves
• Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data
• Boundary Stabilization of Numerical Approximations of the 1-D Variable Coefficients Wave Equation: A Numerical Viscosity Approach
• Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
• On the Asymptotic Spectrum of Finite Element Matrix Sequences
• Singular Optimal Control for a Transport-Diffusion Equation
• Solutions of the wave equation with localized energy
• Renormalized solutions to the Vlasov equation with coefficients of bounded variation

This page was built for publication: Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach