Inverse hyperbolic problems appear in underwater sound search, geophysics, electrodynamics, etc.
In most practical applications, most of the physical phenomena are modeled by multidimensional equations. Therefore, considerable attention has been devoted to the analysis of multidimensional inverse problems. However, to the best of our knowledge, the solvability of the hyperbolic inverse source problems has only been studied for one-dimensional linear equations.
Ryom Su Jong, a post-graduate student of the Faculty of Applied Mathematics, has investigated the unique solvability of an inverse problem of determining a solely time-dependent source in a multidimensional semilinear hyperbolic equation.
This inverse problem models the identification of underwater sound source when its position is known. She addressed a numerical scheme together with the existence and uniqueness of the weak solution by means of Rothe’s time-discretization method. Moreover, she evaluated the error of the semi-discretization scheme.
The time-discretization method she applied is a powerful and efficient tool for solving a wide range of evolution equations.
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