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

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....

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Detalles Bibliográficos
Autores principales: Yuldashev, T. K., Abdullaev, O. Kh.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Pleiades Publishing 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8189280/
http://dx.doi.org/10.1134/S1995080221050218
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author Yuldashev, T. K.
Abdullaev, O. Kh.
author_facet Yuldashev, T. K.
Abdullaev, O. Kh.
author_sort Yuldashev, T. K.
collection PubMed
description 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.
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spelling pubmed-81892802021-06-10 Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms Yuldashev, T. K. Abdullaev, O. Kh. Lobachevskii J Math Article 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. Pleiades Publishing 2021-06-09 2021 /pmc/articles/PMC8189280/ http://dx.doi.org/10.1134/S1995080221050218 Text en © Pleiades Publishing, Ltd. 2021 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Yuldashev, T. K.
Abdullaev, O. Kh.
Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
title Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
title_full Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
title_fullStr Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
title_full_unstemmed Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
title_short Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
title_sort unique solvability of a boundary value problem for a loaded fractional parabolic-hyperbolic equation with nonlinear terms
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8189280/
http://dx.doi.org/10.1134/S1995080221050218
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