Results 11 to 20 of about 176 (89)

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

Quasilinear elliptic equations with critical potentials

Advances in Nonlinear Analysis, 2017
We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj   +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

Hessian equations of Krylov type on compact Hermitian manifolds

Open Mathematics, 2022
In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix.
Zhou Jundong, Chu Yawei
doaj   +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

Liouville-type theorem for some nonlinear systems in a half-space

Journal of Inequalities and Applications, 2014
In this paper we consider the following Hardy-Littlewood-Sobolev (HLS)-type system of nonlinear equations in the half-space R+n: u(x)=∫R+n(1|x−y|n−α−1|x∗−y|n−α)vq(y)dy, v(x)=∫R+n(1|x−y|n−α−1|x∗−y|n−α)up(y)dy, where p,q>1 and x∗ is the reflection of x ...
Linfen Cao, Zhaohui Dai, Wenyan Li
semanticscholar   +2 more sources

On global existence and nonexistence of solutions to a quasi-linear wave equation with memory, nonlinear damping and source terms

Scientific African, 2021
In this paper, we consider a quasi-linear wave equation with memory, nonlinear source and damping termsutt−Δut−∑i=1n∂∂xiσi(uxi)+∫0tm(t−s)Δuds+f(ut)=g(u).Under some polynomial growth conditions on the nonlinear functions σi(i=1,2,…,n),  f and g, we obtain
Paul A. Ogbiyele
doaj   +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