The numerical solution of forward and inverse Robin problems for Laplace’s equation
Boundary Value Problems, 2019 The Robin boundary value problem for Laplace’s equation in the elliptic region (which is a forward problem) and its related inverse problem can be used to reconstruct Robin coefficients from measurements on a partial boundary (inverse problem).
Dan Qu, Yan-Bo Ma
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The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph
Mathematics, 2022 We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator.
Xian-Biao Wei +2 more
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Multigrid Method for Solving Inverse Problems for Heat Equation
Mathematics, 2022 In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed.
Hassan K. Ibrahim Al-Mahdawi +5 more
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Inverse nodal and inverse spectral problems for discontinuous boundary value problems
Journal of Mathematical Analysis and Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shieh, Chung-tsun, Yurko, V. A.
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Interior Elastic Scattering by a Non-Penetrable Partially Coated Obstacle and Its Shape Recovering
Mathematics, 2021 In this paper, the interior elastic direct and inverse scattering problem of time-harmonic waves for a non-penetrable partially coated obstacle placed in a homogeneous and isotropic medium is studied.
Angeliki Kaiafa, Vassilios Sevroglou
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Inverse boundary-value problems: Elliptic equations
Journal of Mathematical Analysis and Applications, 1970 AbstractInverse, or identification, problems are currently receiving a great deal of attention in virtually all scientific disciplines. Most of the work done so far has dealt with systems governed by ordinary differential equations. This paper points out that the methods most commonly used for these problems are not suitable for inverse problems ...
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Linearized boundary control method for an acoustic inverse boundary value problem
Inverse Problems, 2022 Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of ...
Lauri Oksanen, Tianyu Yang, Yang Yang
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A spacetime collocation Trefftz method for solving the inverse heat conduction problem
Advances in Mechanical Engineering, 2019 In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points ...
Cheng-Yu Ku +4 more
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On the Numerical Solution of a Hyperbolic Inverse Boundary Value Problem in Bounded Domains
Mathematics, 2022 We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation.
Roman Chapko, Leonidas Mindrinos
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An inverse boundary-value problem for semilinear elliptic equations
Electronic Journal of Differential Equations, 2010 We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded ...
Ziqi Sun
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