Article

Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms

T. K. YuldashevUzbek–Israel Joint Faculty of High Technology and Engineering Mathematics, National University of Uzbekistan named after M. Ulugbek, 100174, Tashkent, UzbekistanO. Kh. AbdullaevInstitute of Mathematics named after V. I. Romanovskii of Academy of Sciences of Uzbekistan, 100174, Tashkent, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2021en

ABI

Abstract

This work is devoted to study the existence and uniqueness of solution of an analogue of the Gellerstedt problem with nonlocal assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation with nonlinear terms and Gerasimov–Caputo operator of differentiation. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of successive approximations of factorial law for Volterra type nonlinear integral equations.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Numerical methods in inverse problems

Identifiers

DOI: 10.1134/s1995080221050218

Citations and references

Cited by 32 27 references

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