An a priori estimate for the solution of a mixed problem for the heat equation

2006 ◽  
Vol 42 (10) ◽  
pp. 1447-1452
Author(s):  
N. Yu. Kapustin
Keyword(s):  
Heat Equation ◽  
Mixed Problem ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate

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 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 A Mixed Problem with an Integral Two-Space-Variables Condition for Parabolic Equation with The Bessel Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Bouziani Abdelfatah ◽  
Oussaeif Taki-Eddine ◽  
Ben Aoua Leila
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
A Priori ◽  
Energy Inequality ◽  
A Priori Estimate ◽  
Bessel Operator ◽  
Priori Estimate ◽  
Uniqueness Of The Solution

We study a mixed problem with an integral two-space-variables condition for parabolic equation with the Bessel operator. The existence and uniqueness of the solution in functional weighted Sobolev space are proved. 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 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.

scholarly journals A Discrete Analog of the Lyapunov Function for Hyperbolic Systems

2018 ◽  
Vol 64 (4) ◽  
pp. 591-602
Author(s):  
R D Aloev ◽  
M U Khudayberganov
Keyword(s):  
Lyapunov Function ◽  
Hyperbolic Systems ◽  
A Priori ◽  
A Priori Estimate ◽  
Discrete Analog ◽  
Priori Estimate ◽  
Constant Coefficients ◽  
The Difference ◽  
Dissipative Boundary ◽  
Linear Hyperbolic System

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analog of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.

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