scholarly journals On a Nonhomogeneous Timoshenko System with Nonlocal Constraints

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Said Mesloub ◽  
Faten Aldosari
Keyword(s):  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Main Concern ◽  
Well Posedness ◽  
Integral Type ◽  
A Priori Bounds ◽  
Timoshenko System ◽  
The Given ◽  
Nonlocal Constraints

Our main concern in this paper is to prove the well posedness of a nonhomogeneous Timoshenko system with two damping terms. The system is supplemented by some initial and nonlocal boundary conditions of integral type. The uniqueness and continuous dependence of the solution on the given data follow from some established a priori bounds, and the proof of the existence of the solution is based on some density arguments.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

Initial-boundary value problems for a time-fractional differential equation with involution perturbation

2019 ◽  
Vol 14 (3) ◽  
pp. 312 ◽  
Author(s):  
Nasser Al-Salti ◽  
Sebti Kerbal ◽  
Mokhtar Kirane
Keyword(s):  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Nonlocal Boundary Conditions ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value ◽  
Formal Solutions ◽  
The Given

Direct and inverse initial-boundary value problems of a time-fractional heat equation with involution perturbation are considered using both local and nonlocal boundary conditions. Results on existence of formal solutions to these problems are presented. Solutions are expressed in a form of series expansions using appropriate orthogonal basis obtained by separation of variables. Convergence of series solutions are obtained by imposing certain conditions on the given data. Uniqueness of the obtained solutions are also discussed. The obtained general solutions are illustrated by an example using an appropriate choice of the given data.

A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Ivan Kiguradze
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order ◽  
Phase Variable ◽  
Differential Inequalities ◽  
Nonlinear Boundary Value Problems ◽  
Estimates Of Solutions ◽  
Priori Estimates

Abstract.For singular in a phase variable second order differential inequalities, a priori estimates of positive solutions, satisfying nonlinear nonlocal boundary conditions, are established.

scholarly journals An Energy Inequality and Its Applications of Nonlocal Boundary Conditions of Mixed Problem for Singular Parabolic Equations in Nonclassical Function Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Moussa Zakari Djibibe ◽  
Kokou Tcharie ◽  
N. Iossifovich Yurchuk
Keyword(s):  
Boundary Conditions ◽  
Mixed Problem ◽  
A Priori Estimates ◽  
A Priori ◽  
Energy Inequality ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Function Spaces ◽  
Priori Estimates ◽  
Singular Parabolic Equations

The aim of this paper is to establish a priori estimates of the following nonlocal boundary conditions mixed problem for parabolic equation: ∂v/∂t-(a(t)/x2)(∂/∂x)(x2∂v/∂x)+b(x,t)v=g(x,t), v(x, 0)=ψ(x), 0≤x≤ℓ, v(ℓ, t)=E(t), 0≤t≤T, ∫0ℓx3v(x,t)dx=G(t), 0≤t≤ℓ. It is important to know that a priori estimates established in nonclassical function spaces is a necessary tool to prove the uniqueness of a strong solution of the studied problems.

scholarly journals A 2.5D MODEL FOR THE EQUATIONS OF THE OCEAN AND THE ATMOSPHERE

2007 ◽  
Vol 05 (03) ◽  
pp. 199-229 ◽  
Author(s):  
Q. S. CHEN ◽  
J. LAMINIE ◽  
A. ROUSSEAU ◽  
R. TEMAM ◽  
J. TRIBBIA
Keyword(s):  
Boundary Conditions ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Primitive Equations ◽  
Well Posedness ◽  
Related Model ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions

The primitive equations (PEs) of the atmosphere and the ocean without viscosity are considered. A 2.5D model is introduced, whose motivation is described in the Introduction. A set of nonlocal boundary conditions is proposed, and well-posedness is established for the flows linearized around a constant velocity stratified flow; homogeneous and nonhomogeneous boundary conditions are considered. A related model of dimension 2.5, of physical interest but with fewer degrees of freedom, is also considered at the end.

scholarly journals On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces

2002 ◽  
Vol 30 (7) ◽  
pp. 435-447 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Nonlocal Boundary Conditions ◽  
Generalized Solution ◽  
Function Spaces ◽  
Singular Parabolic Equations ◽  
Abstract Formulation

The aim of this paper is to prove the existence, uniqueness, and continuous dependence upon the data of a generalized solution for certain singular parabolic equations with initial and nonlocal boundary conditions. The proof is based on an a priori estimate established in nonclassical function spaces, and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.

scholarly journals On a Langevin equation involving Caputo fractional proportional derivatives with respect to another function

2021 ◽  
Vol 7 (1) ◽  
pp. 1273-1292
Author(s):  
Zaid Laadjal ◽  
◽  
Fahd Jarad ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Gamma Function ◽  
Langevin Equation ◽  
Unknown Function ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
The Given ◽  
Derivatives Of ◽  
Theoretical Results

<abstract><p>In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.</p></abstract>

scholarly journals A Numerical Method for 1-D Parabolic Equation with Nonlocal Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Tadi ◽  
Miloje Radenkovic
Keyword(s):  
Parabolic Equation ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Coordinate Transformation ◽  
Nonlocal Boundary ◽  
Nonlinear Problems ◽  
Nonlocal Boundary Conditions ◽  
Local Method ◽  
One Dimensional ◽  
The Given

This paper is concerned with a local method for the solution of one-dimensional parabolic equation with nonlocal boundary conditions. The method uses a coordinate transformation. After the coordinate transformation, it is then possible to obtain exact solutions for the resulting equations in terms of the local variables. These exact solutions are in terms of constants of integration that are unknown. By imposing the given boundary conditions and smoothness requirements for the solution, it is possible to furnish a set of linearly independent conditions that can be used to solve for the constants of integration. A number of examples are used to study the applicability of the method. In particular, three nonlinear problems are used to show the novelty of the method.

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