Uniqueness for a hyperbolic inverse problem with angular control on the coefficients
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In this article, it was shown that q1 = q2 on the annular region R ≤ |x| ≤ (R + T)/2 provided there is a γ > 0, independent of r.Abstract:
Abstract Suppose qi (x), i = 1, 2 are smooth functions on and Ui (x, t) the solutions of the initial value problem , Ui (x, t) = 0 for t < 0. Pick R, T so that 0 < R < T and let C be the vertical cylinder {(x, t) : |x| = R, R ≤ t ≤ T}. We show that if (U 1, U 1r ) = (U 2, U 2r ) on C then q1 = q2 on the annular region R ≤ |x| ≤ (R + T)/2 provided there is a γ > 0, independent of r, so that ∫|x| = r | Δ S (q1 – q2 )|2 dSx ≤ γ ∫|x| = r |q1 – q2 |2 dSx for all r ∈ [R, (R + T/2)]. Here Δ S is the spherical Laplacian on |x| = r.read more
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Book ChapterDOI
Boundary Value Problems of Mathematical Physics
TL;DR: In this article, the boundary value problems of mathematical physics can be solved by the methods of the preceding chapters by solving a variety of specific problems that illustrate the principal types of problems that were formulated in Chapter 7.
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Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets
Matti Lassas,Lauri Oksanen +1 more
TL;DR: In this article, the authors considered the inverse problem to determine a smooth compact Riemannian manifold with boundary (M,g) from a restriction ΛS,R of the Dirichlet-to-Neumann operator for the wave equation on the manifold.
Journal ArticleDOI
Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets
Matti Lassas,Lauri Oksanen +1 more
TL;DR: In this paper, the authors considered the inverse problem to determine a smooth compact Riemannian manifold with boundary from a restriction of the Dirichlet-to-Neumann operator for the wave equation on the manifold.
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Application of meshfree methods for solving the inverse one-dimensional Stefan problem
TL;DR: In this paper, the authors employ two interpolation techniques to obtain space-time approximate solution for temperature distribution on irregular domains, as well as for the reconstruction of the functions describing the temperature and the heat flux on the fixed boundary x = 0 when the position of the moving interface is given as extra specification.
References
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TL;DR: In this paper, the authors propose a wave equation on n-dimensional space-times for the distribution of discontinuities in differential geometry and derive fundamental solutions to the wave equation.