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 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 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 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 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.

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 The Solvability of First Type Boundary Value Problem for a Schrödinger Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 211-220
Author(s):  
Nigar Yildirim Aksoy
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Uniqueness Theorems ◽  
Priori Estimate ◽  
Type Boundary

AbstractThe paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.

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 On weak solutions of semilinear hyperbolic-parabolic equations

1996 ◽  
Vol 19 (4) ◽  
pp. 751-758 ◽  
Author(s):  
Jorge Ferreira
Keyword(s):  
Parabolic Equation ◽  
Continuous Function ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
A Priori ◽  
A Priori Estimate ◽  
Dirichlet Boundary Conditions ◽  
Priori Estimate

In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation(K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=fwith null Dirichlet boundary conditions and zero initial data, whereF(s)is a continuous function such thatsF(s)≥0,∀s∈Rand{A(t);t≥0}is a family of operators ofL(H01(Ω);H−1(Ω)). For the existence we apply the Faedo-Galerkin method with an unusual a priori estimate and a result of W. A. Strauss. Uniqueness is proved only for some particular classes of functionsF.

A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model

2014 ◽  
Vol 6 (3) ◽  
pp. 281-298 ◽  
Author(s):  
Hai-Yan Cao ◽  
Zhi-Zhong Sun ◽  
Xuan Zhao
Keyword(s):  
Difference Scheme ◽  
Hyperbolic Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Second Order ◽  
Priori Estimate ◽  
Third Order ◽  
The Third ◽  
The Difference ◽  
Second Order Convergence

AbstractThis article deals with the numerical solution to the magneto-thermo-elasticity model, which is a system of the third order partial differential equations. By introducing a new function, the model is transformed into a system of the second order generalized hyperbolic equations. A priori estimate with the conservation for the problem is established. Then a three-level finite difference scheme is derived. The unique solvability, unconditional stability and second-order convergence inL∞-norm of the difference scheme are proved. One numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.

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