APPLICATION OF THE METHOD OF ADDITIONAL ARGUMENT TO ONE INVERSE BOUNDARY VALUE PROBLEM FOR NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

This study examines an inverse boundary value problem for a first-order nonlinear partial integro-differential equation with a nonlinear right-hand side. Using the method of additional arguments, the equivalence of inverse boundary value problems to a system of integral equations is established. A solvability condition was obtained, and the existence and uniqueness of the solution were proven. This method effectively determines unknown functions under given boundary conditions, crucial for solving complex mathematical models. The convergence and stability conditions were analyzed. The results show that this approach simplifies the process of finding solutions and expands the possibilities of analysis for engineering applications.