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 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 Priori Estimation of the Solution for Mixed Problems with Integral Condition for Singular Parabolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Raid Almomani
Keyword(s):  
Parabolic Equations ◽  
Chemical Engineering ◽  
Initial Conditions ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Nonlocal Boundary Conditions ◽  
Mixed Problems ◽  
A Priori Estimation ◽  
Singular Parabolic Equations

We prove a theorem in which we get a priori estimation of the solution for mixed problems with integral condition for singular parabolic equations. Mixed problems with nonlocal boundary conditions or with nonlocal initial conditions were studied in many works lately. Our result plays an important role in the theory of heat transmission, thermoelasticity, chemical engineering, underground water flow, and plasma physics.

scholarly journals On a class of nonclassical hyperbolic equations with nonlocal conditions

2002 ◽  
Vol 15 (2) ◽  
pp. 125-140 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Continuous Dependence ◽  
Hyperbolic Equations ◽  
Initial Conditions ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
A Priori Estimate ◽  
Analysis Method ◽  
Priori Estimate ◽  
Abstract Formulation

This paper proves the existence, uniqueness and continuous dependence of a solution of a class of nonclassical hyperbolic equations with nonlocal boundary and initial conditions. Results are obtained by using a functional analysis method based on an a priori estimate and on the density of the range of the linear operator corresponding to the abstract formulation of the considered problem.

scholarly journals On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations

2002 ◽  
Vol 7 (10) ◽  
pp. 517-530 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Point Boundary ◽  
Priori Estimate ◽  
Weighted Integral ◽  
Singular Parabolic Equations

We deal with a three point boundary value problem for a class of singular parabolic equations with a weighted integral condition in place of one of standard boundary conditions. We will first establish an a priori estimate in weighted spaces. Then, we prove the existence, uniqueness, and continuous dependence of a strong solution.

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