Unique continuation on a line for the Helmholtz equation

DOI10.1080/00036811.2011.581235zbMath1251.65153OpenAlexW1965538060WikidataQ58243671 ScholiaQ58243671MaRDI QIDQ3167670

Boxi Xu, Shuai Lu, Xiang Xu

Publication date: 2 November 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2011.581235

zbMATH Keywords

unique continuationHelmholtz equationline continuation

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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Cites Work

• Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods
• Unique continuation on a hyperplane for wave equation
• Regularization tools version \(4.0\) for matlab \(7.3\)
• A collocation method for boundary value problems
• A unique continuation theorem for uniformly elliptic equations with strongly singular potentials
• Increased stability in the continuation of solutions to the Helmholtz equation
• On the unique continuation theorem for certain second and fourth order elliptic equations
• The conditional stability in line unique continuation for a wave equation and an inverse wave source problem
• Elliptic Partial Differential Equations of Second Order
• Unique continuation on a line for harmonic functions
• Stability in line unique continuation of harmonic functions: general dimensions
• UNIQUENESS ALONG A LINE FOR AN INVERSE WAVE SOURCE PROBLEM

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