Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. A plurality of nonlinear equations in partial derivatives having a Lax pair are either exactly integrable or equations that allow rich classes of exact solutions.
T. V. Red'kina, O. V. Novikova
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The Maximal Regularity of Nonlinear Second-Order Hyperbolic Boundary Differential Equations
AxiomsIn this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if ...
Xingyu Liu
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Derivation and analysis of a fluid-dynamical model in thin and long elastic vessels
Networks and Heterogeneous Media, 2006 Starting from the three-dimensional Newtonian and incompressible Navier-Stokes equations in a compliant straight vessel, we derive a reduced one-dimensional model by an averaging procedure which takes into consideration the elastic properties of the wall
Debora Amadori +2 more
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On the Continuous Generalized Solutions of a Lossless Transmission Line System with Josephson Junction [PDF]
Results in Nonlinear Analysis, 2018 The present paper is devoted to the investigation of lossless transmission lines with Josephson junction. Such lines are described by first order nonlinear hyperbolic system partial differential equations.
Ljubomir P. Georgiev
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BACKLUND TRANSFORMATIONS FOR LIOUVILLE’S EQUATIONS WITH EXPONENTIAL NONLINEARITY
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. The study of Backlund 's transformations is one of the current topics in the theory of differential equations in partial derivatives. Such transformations are used to find solutions to nonlinear differential equations, including solitonic ...
T. V. Red'kina, O. V. Novikova
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On the construction and properties of WENO schemes order five, seven, nine, eleven and thirteen. Part 2. Numerical examples [PDF]
Компьютерные исследования и моделирование, 2016 WENO schemes (weighted, essentially non oscillating) are currently having a wide range of applications as approximate high order schemes for discontinuous solutions of partial differential equations. These schemes are used for direct numerical simulation
Nikolay Mikhaylovitch Evstigneev
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On numerical methods for one problem of mixed type
Mathematical Modelling and Analysis, 2001 This article is devoted to further investigation of numerical methods for one differential problem of mixed type. We consider a two‐dimensional first‐order differential equation with one complex‐valued and one real constant coefficients.
S. Sytova
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A parabolic-hyperbolic free boundary problem modeling tumor growth with drug application
Electronic Journal of Differential Equations, 2010 In this article, we study a free boundary problem modeling the growth of tumors with drug application. The model consists of two nonlinear second-order parabolic equations describing the diffusion of nutrient and drug concentration, and three ...
Ji-Hong Zhao
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Nonlinear monotonization of the Babenko scheme for the quasi‐linear advection equation
Mathematical Modelling and Analysis, 2005 The paper is devoted to construction and development of new method for numerical solution of hyperbolic type equations [14, 17]. In the previous papers [4, 5, 6, 7, 8, 9] authors have investigated theoretically and tested experimentally 26 different ...
T. A. Alexandrikova, M. P. Galanin
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Existence of bounded solutions for nonlinear hyperbolic partial differential equations
Electronic Journal of Differential Equations, 2015 In this article we first establish a new representation formula for bounded solutions to a class of nonlinear second-order hyperbolic partial differential equations.
Toka Diagana, Mamadou Moustapha Mbaye
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