An Inverse Problem for a Hyperbolic Integro-DifferentialEquation in a Bounded Domain
J. Sh. SafarovV. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic
of Uzbekistan, Tashkent, 100174, UzbekistanD. K. DurdievV. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic
of Uzbekistan, Tashkent, 100174, UzbekistanАскар Ахмадович РахмоновV. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic
of Uzbekistan, Tashkent, 100174, Uzbekistan
Ochiq kirish: yoʻq
ABI
Annotatsiya
We consider the inverse problem of finding the kernel of the integral term in an integro-differential equation. The problem of finding the memory kernel in the wave process is reduced to a nonlinear Volterra integral equation of the first kind of convolution type, which is in turn reduced under some assumptions to a Volterra integral equation of the second kind. Using the method of contraction mappings, we prove the unique solvability of the problem in the space of continuous functions with weighted norms and obtain an estimate of the conditional stability of the solution.
Hali tarjima qilinmagan