Results 11 to 20 of about 62 (62)

A mixed problem with only integral boundary conditions for a hyperbolic equation

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 24, Page 1279-1291, 2004., 2004
We investigate an initial boundary value problem for a second‐order hyperbolic equation with only integral conditions. We show the existence, uniqueness, and continuous dependence of a strongly generalized solution. The proof is based on an energy inequality established in a nonclassical function space, and on the density of the range of the operator ...
Abdelfatah Bouziani
wiley   +1 more source

On a class of nonlinear reaction‐diffusion systems with nonlocal boundary conditions

Abstract and Applied Analysis, Volume 2004, Issue 9, Page 793-813, 2004., 2004
We prove the existence, uniqueness, and continuous dependence of a generalized solution of a nonlinear reaction‐diffusion system with only integral terms in the boundaries. We first solve a particular case of the problem by using the energy‐integral method. Next, via an iteration procedure, we derive the obtained results to study the solvability of the
Abdelfatah Bouziani
wiley   +1 more source

On the weak solution of a three‐point boundary value problem for a class of parabolic equations with energy specification

Abstract and Applied Analysis, Volume 2003, Issue 10, Page 573-589, 2003., 2003
This paper deals with weak solution in weighted Sobolev spaces, of three‐point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation.
Abdelfatah Bouziani
wiley   +1 more source

Rothe method for a mixed problem with an integral condition for the two‐dimensional diffusion equation

Abstract and Applied Analysis, Volume 2003, Issue 16, Page 899-922, 2003., 2003
This paper deals with an initial boundary value problem with an integral condition for the two‐dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one‐dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by
Nabil Merazga, Abdelfatah Bouziani
wiley   +1 more source

On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator

Journal of Applied Mathematics, Volume 2003, Issue 10, Page 487-502, 2003., 2003
We consider a mixed problem with Dirichlet and integral conditions for a second‐order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the ...
Abdelfatah Bouziani
wiley   +1 more source

Generalized Cahn‐Hilliard equations based on a microforce balance

Journal of Applied Mathematics, Volume 2003, Issue 4, Page 165-185, 2003., 2003
We present some models of Cahn‐Hilliard equations based on a microforce balance proposed by M. Gurtin. We then study the existence and uniqueness of solutions.
Alain Miranville
wiley   +1 more source

Boundary value problem with integral conditions for a linear third‐order equation

Journal of Applied Mathematics, Volume 2003, Issue 11, Page 553-567, 2003., 2003
We prove the existence and uniqueness of a strong solution for a linear third‐order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.
M. Denche, A. Memou
wiley   +1 more source

Initial‐boundary value problem with a nonlocal condition for a viscosity equation

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 6, Page 327-338, 2002., 2002
This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial‐boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the ...
Abdelfatah Bouziani
wiley   +1 more source

On the solvability of parabolic and hyperbolic problems with a boundary integral condition

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 4, Page 201-213, 2002., 2002
We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear ...
Abdelfatah Bouziani
wiley   +1 more source

Boundedness of Solutions to a Parabolic-Elliptic Keller–Segel Equation in ℝ2 with Critical Mass

Advanced Nonlinear Studies, 2018
We consider the Cauchy problem for a parabolic-elliptic system in ℝ2{\mathbb{R}^{2}}, called the parabolic-elliptic Keller–Segel equation, which appears in various fields in biology and physics.
Nagai Toshitaka, Yamada Tetsuya
doaj   +1 more source