Maqola

An Inverse Problem for a Hyperbolic Integro-DifferentialEquation in a Bounded Domain

J. Sh. SafarovTashkent University of Information Technologies, Tashkent, 100084, UzbekistanD. K. DurdievBukhara State University, Bukhara, 200100, UzbekistanАскар Ахмадович РахмоновBukhara State University, Bukhara, 200100, Uzbekistan

Siberian Advances in Mathematicsjournal2024en

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.

Mavzular

Numerical methods in inverse problems Advanced Mathematical Modeling in Engineering Differential Equations and Boundary Problems

Identifikatorlar

DOI: 10.1134/s1055134424020068

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