Abstract:
The forward and inverse problems are investigated for the quasilinear wave equation ${\square u -qu^{2}-K\ast u=0}$ where the kernel $K(x,t)$ is represented in the form $K(x,t)=p(x) K_0(t)$ with $p(x)$ being a continuous function. The inverse problem is devoted to the determination of the compact functions $q(x)$ and $p(x)$. Traces of the derivative with respect to $x$ of two solutions to the forward initial–boundary value problem related to two arbitrary boundary data are given for $x=0$ on the finite segment $[0,T]$ as an additional information for the solution to the inverse problem. The conditions for the unique solvability of the forward problem
Keywords:nonlinear wave equation, integro-differential equation, equation with memory, forward problem, inverse problem, existence of solution.
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