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 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.

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 Boundary value problems with nonlocal conditions for hyperbolic systems of equations with two independent variables

2020 ◽  
Vol 53 (2) ◽  
pp. 159-180
Author(s):  
V. M. Kyrylych ◽  
O. Z. Slyusarchuk
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Problems ◽  
Priori Estimates ◽  
Smooth Coefficients

Nonlocal boundary value problems for arbitrary order hyperbolic systems with one spatial variable are considered. A priori estimates for general nonlocal mixed problems for systems with smooth and piecewise smooth coefficients are obtained. The correct solvability of such problems is proved.Examples of additional conditions necessity are provided.

scholarly journals Uniform a priori estimates for elliptic problems with impedance boundary conditions

2020 ◽  
Vol 19 (5) ◽  
pp. 2445-2471
Author(s):  
Théophile Chaumont-Frelet ◽  
◽  
Serge Nicaise ◽  
Jérôme Tomezyk ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Priori Estimates

scholarly journals On the Solvability of a Mixed Problem for a High-Order Partial Differential Equation with Fractional Derivatives with Respect to Time, with Laplace Operators with Spatial Variables and Nonlocal Boundary Conditions in Sobolev Classes

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 235 ◽  
Author(s):  
Onur İlhan ◽  
Shakirbay Kasimov ◽  
Shonazar Otaev ◽  
Haci Baskonus
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Fractional Derivatives ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Order Partial Differential Equation ◽  
Sobolev Classes ◽  
Spatial Variables

In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes.

scholarly journals A QUANTUM TRANSMITTING SCHRÖDINGER–POISSON SYSTEM

2004 ◽  
Vol 16 (03) ◽  
pp. 281-330 ◽  
Author(s):  
M. BARO ◽  
H.-CHR. KAISER ◽  
H. NEIDHARDT ◽  
J. REHBERG
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Real Axis ◽  
A Priori Estimates ◽  
A Priori ◽  
Poisson System ◽  
Transparent Boundary Conditions ◽  
Bounded Interval ◽  
Zero Current ◽  
Priori Estimates

We study a stationary Schrödinger–Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows us to model a non-zero current through the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

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