Global Uniqueness and Stability for a Class of Multidimesional Inverse Hyperbolic Problems with Two Unknowns
نویسندگان
چکیده
In this paper, we obtain the global uniqueness and stablity estimate for a class of multidimensional inverse hyperbolic problems of determining source terms 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 the compactness/uniqueness argument, we can prove the uniqueness and the stability by a new kind of unique continuation property of a non-local hyperbolic equation. ∗Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro Tokyo 153 Japan. E-mail: [email protected]. †School of Mathematics, Sichuan University, Chengdu 610064, China; and Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid Spain. This author is partially supported by NSF of China under grant 19901024 and the Postdoctoral Fellowship of the Spanish Education and Culture Ministry. E-mail: [email protected]. 1
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