On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 181
Author(s):  
Abdelkader Djerad ◽  
Ameur Memou ◽  
Ali Hameida
Keyword(s):  
Iterative Process ◽  
Linear Problem ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Well Posedness ◽  
Analysis Method ◽  
Integral Conditions ◽  
Priori Estimate ◽  
Mixed Problems

The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.

scholarly journals Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelkader Djerad ◽  
Ameur Memou ◽  
Ali Hameida
Keyword(s):  
Linear Problem ◽  
A Priori ◽  
Nonlinear Problems ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Well Posedness ◽  
Analysis Method ◽  
Integral Conditions ◽  
Priori Estimate ◽  
Mixed Problems

AbstractThe aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and the density of the operator range generated by the considered problem is proved by using the functional analysis method. Subsequently, by applying an iterative process based on the obtained results for the linear problem, the existence, uniqueness of the weak solution of the nonlinear problems is established.

scholarly journals Mixed problem with integral conditions for a certain class of hyperbolic equations

2001 ◽  
Vol 1 (3) ◽  
pp. 107-116 ◽  
Keyword(s):  
Mixed Problem ◽  
Continuous Dependence ◽  
Hyperbolic Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Generalized Solution ◽  
Two Dimensional ◽  
Analysis Method ◽  
Integral Conditions ◽  
Priori Estimate

We study a mixed problem with purely integral conditions for a class of two-dimensional second-order hyperbolic equations. We prove the existence, uniqueness, and the continuous dependence upon the data of a generalized solution. We use a functional analysis method based on a priori estimate and on the density of the range of the operator generated by the considered problem.

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

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 Mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator

2002 ◽  
Vol 15 (3) ◽  
pp. 277-286 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Continuous Dependence ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Bessel Operator ◽  
Analysis Method ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we prove the existence, uniqueness and continuous dependence on the data of a solution of a mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator. The proof uses a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the considered problem.

scholarly journals Mixed Problem with an Integral Two-Space-Variables Condition for a Class of Hyperbolic Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Taki-Eddine Oussaeif ◽  
Abdelfatah Bouziani
Keyword(s):  
Classical Solution ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Energy Inequality ◽  
A Priori Estimate ◽  
Neumann Condition ◽  
Priori Estimate ◽  
Mixed Problems

This paper is devoted to the proof of the existence and uniqueness of the classical solution of mixed problems which combine Neumann condition and integral two-space-variables condition for a class of hyperbolic equations. The proof is based on a priori estimate “energy inequality” and the density of the range of the operator generated by the problem considered.

scholarly journals A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS

2019 ◽  
pp. 41-47
Author(s):  
Л.М. Энеева
Keyword(s):  
Fractional Derivatives ◽  
Model Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Equation Of Motion ◽  
Point Boundary ◽  
Priori Estimate ◽  
Fractal Media ◽  
Different Origins ◽  
Variable Potential

В работе исследуется обыкновенное дифференциальное уравнение дробного порядка, содержащее композицию дробных производных с различными началами, с переменным потенциалом. Рассматриваемое уравнение выступает модельным уравнением движения во фрактальной среде. Для исследуемого уравнения доказана априорная оценка решения смешанной двухточечной краевой задачи. We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.

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