Global uniqueness theorems for linear and nonlinear waves

DOI10.1016/j.jfa.2015.08.012zbMath1329.35007arXiv1412.1537OpenAlexW2139336498MaRDI QIDQ746916

Arick Shao, Spyridon Alexakis

Publication date: 21 October 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.1537

zbMATH Keywords

wave equationnonlinear wavesKlein-Gordon equationunique continuationradiation fieldCarleman-type estimatesexterior domain of a light conesubconformal focusing-type equationssuperconformal defocusing type equations

Mathematics Subject Classification ID

Wave equation (35L05) A priori estimates in context of PDEs (35B45) Waves and radiation in optics and electromagnetic theory (78A40) Continuation and prolongation of solutions to PDEs (35B60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (13)

Resolvent estimates for spacetimes bounded by Killing horizons ⋮ Lorentzian Calderón problem under curvature bounds ⋮ Unique continuation from infinity in asymptotically anti-de Sitter spacetimes ⋮ On the rigidity from infinity for nonlinear Alfvén waves ⋮ On the profile of energy concentration at blow-up points for subconformal focusing nonlinear waves ⋮ A gauge-invariant unique continuation criterion for waves in asymptotically anti-de Sitter spacetimes ⋮ A uniqueness theorem for 3D semilinear wave equations satisfying the null condition ⋮ The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes ⋮ Carleman estimate for ultrahyperbolic operators and improved interior control for wave equations ⋮ Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials ⋮ Unnamed Item ⋮ On controllability of waves and geometric Carleman estimates ⋮ An inverse scattering theorem for (1 + 1)-dimensional semi-linear wave equations with null conditions

Cites Work

• Unnamed Item
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• Uniqueness results for ill-posed characteristic problems in curved space-times
• Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
• A non uniqueness result for operators of principal type
• Lower bounds for solutions of Schrödinger equations
• Über periodische nichtsinguläre Lösungen in der allgemeinen Relativitätstheorie
• Über zeitabhängige Lösungen der Feldgleichungen der allgemeinen Relativitätstheorie
• Growth properties of solutions of the reduced wave equation with a variable coefficient
• On asymptotically flat solutions of Einstein's equations periodic in time: I. Vacuum and electrovacuum solutions
• Global solutions of nonlinear hyperbolic equations for small initial data
• Radiation fields and hyperbolic scattering theory
• ON THE POSSIBLE RATE OF DECAY AT INFINITY OF SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
• Remark on the asymptotic behavior of the klein gordon equation in ℝⁿ⁺¹
• On the local extension of Killing vector-fields in Ricci flat manifolds
• On asymptotically flat solutions of Einstein's equations periodic in time: II. Spacetimes with scalar-field sources
• On positive eigenvalues of one‐body schrödinger operators
• General Relativity
• Notes on the wave equation on asymptotically Euclidean manifolds

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