Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration

2013 ◽  
Vol 54 (2) ◽  
pp. 251-258 ◽  
Author(s):  
A. L. Kazakov ◽  
A. A. Lempert
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Unsteady Filtration ◽  
Uniqueness Of The Solution

scholarly journals The second boundary value problem in a half-strip for a B-parabolic equation with the Gerasimov–Caputo time derivative

2020 ◽  
pp. 37-50
Author(s):  
Ф.Г. Хуштова
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Integral Transform ◽  
Boundary Value ◽  
Time Derivative ◽  
Half Strip ◽  
Uniqueness Of The Solution ◽  
Solution Representation ◽  
Class Of Functions

В работе исследуется вторая краевая задача в полуполосе для параболического уравнения с оператором Бесселя, действующим по пространственной переменной, и частной производной Герасимова–Капуто по времени. Доказаны теоремы существования и единственности решения рассматриваемой задачи. Представление решения найдено в терминах интегрального преобразования с функцией Райта в ядре. Единственность решения доказана в классе функций быстрого роста. При частных значениях параметров, содержащихся в рассматриваемом уравнении, последнее совпадает с классическим уравнением диффузии. In the present paper, we investigate the second boundary value problem in a half-strip for a parabolic equation with the Bessel operator acting with respect to the spatial variable and the Gerasimov–Caputo partial time derivative. Theorems of existence and uniqueness of the solution of the problem under consideration are proved.The solution representation is found in terms of an integral transform with the Wright function in the kernel. The uniqueness of the solution is proved in the class of functions of rapid growth. The considered equation for particular values of the parameters coincides with the classical diffusion equation.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

2001 ◽  
Vol 6 (1) ◽  
pp. 147-155 ◽  
Author(s):  
S. Rutkauskas
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Second Order ◽  
Type Problem ◽  
Dirichlet Type ◽  
Holder Class ◽  
Uniqueness Of The Solution ◽  
Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

scholarly journals Nonlocal inverse boundary-value problem for a 2D parabolic equation with integral overdetermination condition

2020 ◽  
Vol 12 (1) ◽  
pp. 23-33
Author(s):  
E.I. Azizbayov ◽  
Y.T. Mehraliyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Rectangular Domain ◽  
Unknown Coefficient ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem

This article studies a nonlocal inverse boundary-value problem for a two-dimensional second-order parabolic equation in a rectangular domain. The purpose of the article is to determine the unknown coefficient and the solution of the considered problem. To investigate the solvability of the inverse problem, we transform the original problem into some auxiliary problem with trivial boundary conditions. Using the contraction mappings principle, existence and uniqueness of the solution of an equivalent problem are proved. Further, using the equivalency, the existence and uniqueness theorem of the classical solution of the original problem is obtained.

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