A method for finding coefficients of a quasilinear hyperbolic equation |
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Authors: | A Yu Shcheglov |
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Institution: | (1) Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | The inverse problem of finding the coefficients q(s) and p(s) in the equation u tt = a 2 u xx + q(u)u t ? p(u)u x is investigated. As overdetermination required in the inverse setting, two additional conditions are set: a boundary condition and a condition with a fixed value of the timelike variable. An iteration method for solving the inverse problem is proposed based on an equivalent system of integral equations of the second kind. A uniqueness theorem and an existence theorem in a small domain are proved for the inverse problem to substantiate the convergence of the algorithm. |
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Keywords: | quasilinear hyperbolic equation inverse problem for two coefficients iteration method |
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