An inverse boundary value problem for a nonlinear wave equation

Gen Nakamura; Michiyuki Watanabe

doi:10.3934/ipi.2008.2.121

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2008, Volume 2, Issue 1: 121-131. Doi: 10.3934/ipi.2008.2.121

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An inverse boundary value problem for a nonlinear wave equation

Gen Nakamura^1, and
Michiyuki Watanabe^2,

1.
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810
2.
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba, 278-8510

Received: May 31, 2007

Published: January 2008

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Abstract

An inverse boundary value problem for nonlinear wave equation of divergence form in one space dimension is considered. By assuming the nonlinear term is unknown, we show the linear and quadratic part of this term can be identified from the Dirichlet to Neumann map. Here, the nonlinearity is only in terms of the first derivative with respect to the space variable, and the linear and quadratic parts are defined in terms of this derivative. The identification not only gives the uniqueness but also the reconstruction.

Keywords:

Inverse boundary value problems,
Nonlinear Wave equations.

Mathematics Subject Classification: Primary: 35R30, 35L70; Secondary: 35L20.

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