Results 11 to 20 of about 1,188 (55)
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
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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
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Global $L^{p}$ estimates for degenerate Ornstein-Uhlenbeck operators with variable coefficients [PDF]
, 2012 We consider a class of degenerate Ornstein-Uhlenbeck operators in $\mathbb{R}^{N}$, of the kind [\mathcal{A}\equiv\sum_{i,j=1}^{p_{0}}a_{ij}(x) \partial_{x_{i}x_{j}}^{2}+\sum_{i,j=1}^{N}b_{ij}x_{i}\partial_{x_{j}}%] where $(a_{ij})$ is symmetric ...
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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
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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
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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
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On some nonlinear elliptic systems with coercive perturbations in RN [PDF]
, 2003 A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN: Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.A nonlinear elliptic system involving the p ...
El Manouni, Said, Touzani, Abdelfattah
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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
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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
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