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 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 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.

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 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 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 locally one-dimensional scheme for a general parabolic equation describing microphysical processes in convective clouds

2021 ◽  
Vol 21 (4) ◽  
pp. 45-55
Author(s):  
B.A. Ashabokov ◽  
◽  
A.Kh. Khibiev ◽  
M.Kh. Shkhanukov-Lafishev ◽  
◽  
...  
Keyword(s):  
Parabolic Equation ◽  
Difference Scheme ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
One Dimensional ◽  
Convective Clouds ◽  
Non Local ◽  
Microphysical Processes

A locally one-dimensional difference scheme for a general parabolic equation in a p-dimensional parallelepiped is considered. To describe microphysical processes in convective clouds, non-local (nonlinear) integral sources of a special type are included in the equation under consideration. An a priori estimate for the solution of a locally one-dimensional scheme is obtained and its convergence is proved.

scholarly journals Mixed problem with boundary integral conditions for a certain parabolic equation

1996 ◽  
Vol 9 (3) ◽  
pp. 323-330 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Parabolic Equation ◽  
Present Article ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Energy Inequality ◽  
Boundary Integral ◽  
Integral Conditions ◽  
Uniqueness Of A Solution

The present article is devoted to a proof of the existence and uniqueness of a solution of a mixed problem with boundary integral conditions for a certain parabolic equation. The proof is based on an energy inequality and on the fact that the range of the operator generated by the problem is dense.

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