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 Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 10, Pages 1571–1579 (Mi zvmmf10095)

Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition

A. M. Denisov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

Abstract: An initial boundary-value problem for a quasilinear system of partial differential equations with a nonlocal boundary condition involving a delayed argument is considered. The existence of a unique solution to this problem is proved by reducing it to a system of nonlinear integral-functional equations. The inverse problem of finding a solution-dependent coefficient of the system from additional information on a solution component specified at a fixed point of space as a function of time is formulated. The uniqueness of the solution of the inverse problem is proved. The proof is based on the derivation and analysis of an integral-functional equation for the difference between two solutions of the inverse problem.

Key words: quasilinear system of partial differential equations, nonlocal boundary condition, delayed argument, inverse problem, uniqueness of solution.

DOI: https://doi.org/10.7868/S004446691410007X

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:10, 1513–1521

Bibliographic databases:

UDC: 519.63

Citation: A. M. Denisov, “Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition”, Zh. Vychisl. Mat. Mat. Fiz., 54:10 (2014), 1571–1579; Comput. Math. Math. Phys., 54:10 (2014), 1513–1521

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/zvmmf/v54/i10/p1571

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. T. K. Yuldashev, “Obratnaya zadacha dlya nelineinogo integro-differentsialnogo uravneniya Fredgolma chetvertogo poryadka s vyrozhdennym yadrom”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:4 (2015), 736–749
2. A. M. Denisov, “Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition containing a retarded argument”, Differ. Equ., 51:9 (2015), 1126–1136