Inverse problem for a loaded diffusion-wave equation with the Caputo fractional derivative
Inverse problem for a loaded diffusion-wave equation with the Caputo fractional derivative
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 23, 1, pp. 343-353 (2026)
Abstract:
In this work, we discuss an inverse problem with a nonlinear gluing condition for a loaded diffusion-wave equation with two lines of changing type, containing a nonlinear loaded term. Uniqueness and existence are proven using theories of integral equations and the methods of successive approximations and compressed mappings. The necessary classes and sufficient conditions for the given functions are determined to ensure the unique solvability of the problem under study.
Keywords: inverse problem, loaded diffusion-wave equation, non linear loaded, non linear gluing condition, uniqueness and existence