Inverse source problem for a Hopf-type system

A. Mukimov; B. Mamasoliyev; Kh. Imomnazarov; I. Iskandarov

doi:10.29229/uzmj.2026-1-15

Inverse source problem for a Hopf-type system

Authors

A. Mukimov Author
B. Mamasoliyev Author
Kh. Imomnazarov Author
I. Iskandarov Author

DOI:

https://doi.org/10.29229/uzmj.2026-1-15

Keywords:

Two-velocity hydrodynamics, viscous fluid, relative velocity, direct problem, inverse problem, Darcy coefficient

Abstract

A one-dimensional inverse problem for a quasilinear hyperbolic system with an unknown excitation source is considered. The Cauchy problem for a nonlinear Hopf-type system is studied. A Fourier transform is used to reduce the inverse problem to a direct problem, and an existence and uniqueness theorem for the solution is proved. The approach used can form the basis for constructing an efficient numerical algorithm for the inverse problem.