Global Uniqueness and Stability for a Class of Multidimensional Inverse Hyperbolic Problems with Two Unknowns

Global Uniqueness and Stability for a Class of Multidimensional Inverse Hyperbolic Problems with... In this paper we obtain the global uniqueness and stability estimate for a class of multidimensional inverse hyperbolic problems of determining a source term and an initial value from a single measurement of boundary values or interior values. By means of a suitable transformation, we reduce the problem to the observability inequalities for nonconservative hyperbolic equations with memory. Then, using a compactness/uniqueness argument, we can prove the uniqueness and the stability by a new kind of unique continuation property of a nonlocal hyperbolic equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Global Uniqueness and Stability for a Class of Multidimensional Inverse Hyperbolic Problems with Two Unknowns

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Publisher
Springer-Verlag
Copyright
Copyright © 2003 by Springer-Verlag
Subject
Philosophy
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-003-0775-5
Publisher site
See Article on Publisher Site

Abstract

In this paper we obtain the global uniqueness and stability estimate for a class of multidimensional inverse hyperbolic problems of determining a source term and an initial value from a single measurement of boundary values or interior values. By means of a suitable transformation, we reduce the problem to the observability inequalities for nonconservative hyperbolic equations with memory. Then, using a compactness/uniqueness argument, we can prove the uniqueness and the stability by a new kind of unique continuation property of a nonlocal hyperbolic equation.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2003

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