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Volume 9
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Article

Study of the Boundary Value Problems for Nonlinear Wave Equations on Domains with a Complex Structure of the Boundary and Prehistory

by
Vasyl Marynets
1,†,
Kateryna Marynets
2,*,† and
Oksana Kohutych
1,†
1
Faculty of Mathematics and Digital Technologies, Uzhhorod National University, Universytetska St. 14, 88000 Uzhhorod, Ukraine
2
Delft Institute of Applied Mathematics, EEMCS, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2021, 9(16), 1888; https://doi.org/10.3390/math9161888
Submission received: 5 July 2021 / Revised: 3 August 2021 / Accepted: 7 August 2021 / Published: 9 August 2021
(This article belongs to the Special Issue Advanced Methods in Computational Mathematical Physics)
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Abstract

We study a boundary value problem for nonlinear partial differential equations of the hyperbolic type on the plain in a domain with a complex boundary. To find the missing data for the given boundary constraints, we solve a supplementary nonlinear problem. For the approximation of solutions, one constructive method is built.
Keywords: nonlinear wave equation; two–sided method; boundary value problem with prehistory; “free” curves nonlinear wave equation; two–sided method; boundary value problem with prehistory; “free” curves

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MDPI and ACS Style

Marynets, V.; Marynets, K.; Kohutych, O. Study of the Boundary Value Problems for Nonlinear Wave Equations on Domains with a Complex Structure of the Boundary and Prehistory. Mathematics 2021, 9, 1888. https://doi.org/10.3390/math9161888

AMA Style

Marynets V, Marynets K, Kohutych O. Study of the Boundary Value Problems for Nonlinear Wave Equations on Domains with a Complex Structure of the Boundary and Prehistory. Mathematics. 2021; 9(16):1888. https://doi.org/10.3390/math9161888

Chicago/Turabian Style

Marynets, Vasyl, Kateryna Marynets, and Oksana Kohutych. 2021. "Study of the Boundary Value Problems for Nonlinear Wave Equations on Domains with a Complex Structure of the Boundary and Prehistory" Mathematics 9, no. 16: 1888. https://doi.org/10.3390/math9161888

APA Style

Marynets, V., Marynets, K., & Kohutych, O. (2021). Study of the Boundary Value Problems for Nonlinear Wave Equations on Domains with a Complex Structure of the Boundary and Prehistory. Mathematics, 9(16), 1888. https://doi.org/10.3390/math9161888

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