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

Journal Article · Wed Oct 15 04:00:00 EDT 2003 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-003-0775-5· OSTI ID:21064231

Yamamoto, Masahiro ^[1]

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1. Department ofMathematical Sciences, University of Tokyo, 3-8-1 KomabaMeguro, Tokyo 153 (Japan)

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.

• OSTI ID: 21064231
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 48; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
MANY-DIMENSIONAL CALCULATIONS
STABILITY
TOPOLOGY
TRANSFORMATIONS