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February  2008, 2(1): 121-131. doi: 10.3934/ipi.2008.2.121

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, Japan
2. 

Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba, 278-8510, Japan

Received  June 2007 Published  January 2008

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: 35L2.
Citation: Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems & Imaging, 2008, 2 (1) : 121-131. doi: 10.3934/ipi.2008.2.121
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