scholarly journals Convergence Results on the Boundary Conditions for 2D Large-Scale Primitive Equations in Oceanic Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Yuanfei Li
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Weather Prediction ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Convergence Result ◽  
Primitive Equations ◽  
Convergence Results ◽  
Initial Boundary Value

In this paper, the initial boundary value problem for the two-dimensional large-scale primitive equations of large-scale oceanic motion in geophysics is considered, which are fundamental models for weather prediction. By establishing rigorous a priori bounds with coefficients and deriving some useful inequalities, the convergence result for the boundary conditions is obtained.

scholarly journals Continuous Dependence on the Heat Source of 2D Large-Scale Primitive Equations in Oceanic Dynamics

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1961
Author(s):  
Yuanfei Li ◽  
Peng Zeng
Keyword(s):  
Heat Source ◽  
Continuous Dependence ◽  
Large Scale ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Primitive Equations ◽  
Weather And Climate ◽  
Inequality Technique ◽  
Initial Boundary Value

In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

scholarly journals On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator

2003 ◽  
Vol 2003 (10) ◽  
pp. 487-502
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
A Priori Estimate ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Bessel Operator ◽  
Integral Conditions ◽  
Initial Boundary Value

We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.

On convergence and error estimates for the horizontal line method applied to Maxwell's initial boundary problem in anisotropic, inhomogeneous media

1980 ◽  
Vol 86 (1-2) ◽  
pp. 53-59 ◽  
Author(s):  
Rainer Picard
Keyword(s):  
Perturbation Theory ◽  
Error Estimates ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Horizontal Line ◽  
Line Method ◽  
Initial Boundary Problem ◽  
Convergence Results ◽  
Rothe Method ◽  
Initial Boundary Value

SynopsisIn the following paper, the horizontal line method (the Rothe method) is applied to Maxwell's initial boundary value problem. By means of results from abstract perturbation theory, convergence results and error estimates are established.

scholarly journals On Initial Boundary Value Problem for Parabolic Differential Operator with Non-coercive Boundary Conditions

2020 ◽  
pp. 547-558
Author(s):  
Alexander N. Polkovnikov
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Sobolev Type ◽  
Type Spaces ◽  
Bochner Space ◽  
Initial Boundary Value

We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in Rn with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space

scholarly journals ON A 3D INITIAL-BOUNDARY VALUE PROBLEM FOR DETERMINING THE DYNAMICS OF IMPURITIES CONCENTRATION IN A HORIZONTAL LAYERED FINE-PORE MEDIUM

2019 ◽  
Vol 3 ◽  
pp. 60
Author(s):  
Sharif E. Guseynov ◽  
Ruslans Aleksejevs ◽  
Jekaterina V. Aleksejeva
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Analytical Approach ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Unsteady State ◽  
State Boundary ◽  
Initial Boundary Value

In the present paper, we propose an analytical approach for solving the 3D unsteady-state boundary-value problem for the second-order parabolic equation with the second and third types boundary conditions in two-layer rectangular parallelepipedic domain.

scholarly journals A Nonhomogeneous Boundary-Valued Problem for the coupled KDV system

2021 ◽  
Author(s):  
Yitong Pei ◽  
Boling Guo
Keyword(s):  
Boundary Conditions ◽  
Contraction Mapping ◽  
Finite Interval ◽  
Smooth Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Contraction Mapping Principle ◽  
Nonhomogeneous Boundary ◽  
The Laplace Transform ◽  
Initial Boundary Value

In this paper, we study the initial-boundary-value problem (IBVP) for coupled Korteweg-de Vries equations posed on a finite interval with nonhomogeneous boundary conditions. We overcome the requirement for stronger smooth boundary conditions in the traditional method via the Laplace transform. Our approach uses the strong Kato smoothing property and the contraction mapping principle.

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