KM
Authored
17 records found
We present original results in study of the second-order differential equation with exponential non-linearities, subjected to the Dirichlet boundary conditions. Using the proper substitution techniques, we reduce the given problem to the study of its lower and upper solutions.@en
We deal with a system of quasilinear fractional differential equations, subjected to the Cauchy–Nicoletti type boundary conditions. The task of explicit solution of such problems is difficult and not always solvable. Thus we suggest a suitable numerical–analytic technique that al
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We studied one essentially nonlinear two–point boundary value problem for a system of fractional differential equations. An original parametrization technique and a dichotomy-type approach led to investigation of solutions of two “model”-type fractional boundary value problems, c
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We study a boundary value problem for a system of the third order semi-linear partial differential equations with nonlocal boundary conditions. We establish sufficient conditions of existence, uniqueness, regularity and sign-preserving property of solutions of the studied problem
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We investigate the boundary-value problem that models wind-induced equatorial
flows, establishing the existence and uniqueness of solutions. We also discuss some special cases that were studied in recent geophysical research.@en
We study a boundary value problem for a Caputo-type fractional differential equation subjected to periodic boundary conditions. For an auxiliary problem with the simplified right-hand side, we explicitly construct its unique solution. In addition, based on the theory of the topol
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We study a system of non-linear fractional differential equations, subject to integral boundary conditions. We use a parametrization technique and a dichotomy-type approach to reduce the original problem to two “model-type” fractional boundary value problems with linear two-point
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We study boundedness of solutions to a linear boundary value
problem (BVP) modelling a two-layer ocean with a uniform eddy viscosity in
the lower layer and variable eddy viscosity in the upper layer. We analyse
bounds of solutions to the given problem on the examples of different
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The aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and
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We present recent results in study of a mathematical model of the Sea-Breeze flow, arising from a general model of the ‘morning glory’ phenomena. Based on analysis of the Dirichlet spectrum of a corresponding Sturm-Liouville problem and application of the Fredholm alternative, we
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We discuss a mathematical model for the equatorial current across the Pacific Ocean, obtained as a leading-order solution to the Navier-Stokes governing equations for geophysical flows in a rotating frame.@en
We present here exact solutions to the equations of geophysical fluid dynamics that depict inviscid flows moving in the azimuthal direction on a circular path, around the globe, and which admit a velocity profile below the surface and along it. These features render this model su
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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 o
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We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Che
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We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit fun
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We present an approach that facilitates the generation of explicit solutions to atmospheric Ekman flows with a height-dependent eddy viscosity. The approach relies on applying to the governing equations, of Sturm–Liouville type, a suitable Liouville substitution and then reducing
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We present some new results on the approximation of solutions of a special type of fractional boundary-value problem. The focus of our research is a system of three fractional differential equations of the mixed order, subjected to the so-called "interpolation" type boundary rest
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Contributed
3 records found
Mathematical Model of the Arctic Gyre and its Analysis
Exploring the behaviour of a non-linear ordinary differential equation describing the vorticity of Arctic Gyres
In this thesis we consider the incompressible and stationary Stokes problem with Navier-slip boundary conditions on an infinite two-dimensional wedge with opening angle θ. As is common for differential equations on domains with corners, the problem is decomposed into a singular e
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Describing phylogenetic trees or networks with a polynomial is a tool to distinguish between them. In this thesis, a new polynomial for describing rooted binary internally labeled phylogenetic networks and trees is introduced based on the research of P. Liu and J. Pons et al. Two
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