Abstract:
The inverse problem of finding the coefficients $q(s)$ and $p(s)$ in the equation $u_{tt}=a^2u_{xx}+q(u)u_t-p(u)u_x$ 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.
Key words:quasilinear hyperbolic equation, inverse problem for two coefficients, iteration method.
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