Publications (371)
ARTICLE
Well-posedness result for a nonlinear elliptic problem involving variable exponent and Robin type boundary condition.
S. Ouaro, A. Tchousso
We study the following nonlinear elliptic boundary value problem
b(u)−diva(x,∇u)=fa(x,∇u).η=−|u|p(x)−2u in Ω, on ∂Ω,
where Ω is a smooth bounded open domain in ℝN,N≥1 with smooth boundary ∂Ω. We prove the existence and uniqueness of a weak solution for f∈L∞(Ω), the existence and uniqueness of an entropy solution for L1-data f. The functional(...)
Lebesgue and Sobolev spaces with variable exponent; weak solution; entropy solution; Robin type boundary condition
ARTICLE
Weak solutions for anisotropic discrete boundary value problems
B. Koné, S. Ouaro
We prove the existence and uniqueness of weak solutions for a family of discrete boundary value problems for data f which belong to a discrete Hilbert space H. Moreover, as an extension, we prove some existence results of weak solutions for more general data f depending on the solution
discrete boundary value problem; critical point; weak solution
ARTICLE
A symmetrized canonical determinant on odd-class pseudodifferential operators
Marie Françoise Ouedraogo
Inspired by M. Braverman’s symmetrized determinant, we introduce a symmetrized logarithm logsym for certain elliptic
pseudodifferential operators. The symmetrized logarithm of an operator lies in the odd class whenever the operator does. Using the canonical trace extended to log-polyhomogeneous pseudodifferential operators, we define an assoc(...)
pseudodifferentiels operateurs, symmetrized trace, symmetrized determinant, holomorphic familly
ARTICLE
Weak solutions for anisotropic nonlinear elliptic problem with variable exponent and measure data.
B. Koné, S. Ouaro, S. Soma
Let Ω⊂ℝN(N≥3) be a bounded smooth domain and μ be a bounded Radon measure.
In this paper, the authors study the following anisotropic nonlinear boundary value problem:
−∑i=1N∂∂xiai(x,∂u∂xi)=μ in Ω,u|∂Ω=0,
where ai(⋅,⋅):Ω×ℝ→ℝ is a Carathéodory function (i=1,2,…,N) and there exists C1>0 such that
|ai(x,ξ)|≤C1(1+|ξ|pi(x)−1) for all ξ∈ℝ and a.(...)
weak solution; elliptic equation; variable exponent; anisotropic Sobolev spaces; Marcinkiewicz spaces; Radon measure
ARTICLE
Well-posedness results for anisotropic nonlinear elliptic equations with variable exponent and L1-data
S. Ouaro
We study the anisotropic boundary value problem −∑Ni=1∂∂xiai(x,∂∂xiu)=f in Ω, u=0 on ∂Ω, where Ω is a smooth open bounded domain in ℝN (N≥3) and f∈L1(Ω). We prove the existence and uniqueness of an entropy solution for this problem.
anisotropic nonlinear elliptic equations; variable exponent; entropy solution; electrorheological fluids
ARTICLE
Existence and uniqueness of entropy solutions to nonlinear elliptic problems with variable growth
S. Ouaro, S. traoré
The authors study the boundary value problem
{u−div(a(x,∇u))=fu=0inΩ,onΩ,
where Ω is a smooth bounded domain in RN(N≥3) and div(a(x,∇u)) is a p(x)-Laplace type operator. The main results presented are Theorems 3.2 and 4.3, obtained by using variational arguments, which establish the existence and uniqueness of weak energy solutions, for f∈L∞(...)
generalized Lebesgue-Sobolev space; weak energy solution; entropy solution; p(x)-Laplace operator; electrorheological fluid
ARTICLE
Entropy solutions for a doubly nonlinear elliptic problem with variable exponent.
B. K. Bonzi, S. Ouaro
The nonlinear boundary value problem with a p(x)-Laplace type operator under Dirichlet boundary condition is studied. The condition of regularity is relaxed on the variable exponent p(⋅) and on the function b appearing in the governing equation. Although the existence and uniqueness of weak energy solution presented in Section 3 is trivial, an(...)
generalized Lebesgue-Sobolev spaces; weak energy solution; entropy production; p(x)-Laplace operator
ARTICLE
Structural stability for variable exponent elliptic problems. I: The p(x)-Laplacian kind problems
B. Andreianov, M. Bendahmane, S. Ouaro
We study the structural stability (i.e., the continuous dependence on coefficients) of solutions of the elliptic problems under the form
b(un)−divan(x,∇un)=fn.
The equation is set in a bounded domain Ω of ℝN and supplied with the homogeneous Dirichlet boundary condition on ∂Ω. Here b is a non-decreasing function on ℝ, and (an(x,ξ))n is a f(...)
p(x)-Laplacian; Leray-Lions operator; variable exponent; thermorheological fluids; well-posedness; continuous dependence; convergence of minimizers; Young measures
ARTICLE
Structural stability for variable exponent elliptic problems. II: The p(u)-Laplacian and coupled problems
B. Andreianov, M. Bendahmane, S. Ouaro
We study well-posedness for elliptic problems under the form
b(u)−div 𝔞(x,u,∇u)=f,
where 𝔞 satisfies the classical Leray-Lions assumptions with an exponent p that may depend both on the space variable x and on the unknown solution u. A prototype case is the equation u−div (|∇u|p(u)−2∇u)=f.
We have to assume that infx∈Ω⎯⎯⎯⎯⎯,z∈ℝp(x,z) is gre(...)
variable exponent; p(u)-Laplacian; thermorheological fluids; well-posedness; Young measures
ARTICLE
Generalisation of SBA (SOME Blaise-ABBO) algorithme for solving Cauchy nonlinear PDE (Partial Differential Equation) in n (n≥2) dimension space
PARE Youssouf, Francis BASSONO et Blaise SOME
In this paper, we propose a generalisation of the SOME Blaise-ABBO (SBA) method for the resolutionof some strongly non linearevolutive Cauchy partial differential equations (PDEs) in n (n≥2) dimension space like.
Adomian method, Picard principle, successive approximation method, SBA (Some Blaise-Abbo) method
ARTICLE
Well-posedness results for triply nonlinear degenerate parabolic equations.
B. Andreianov, M. Bendahmane, K.H. Karlsen, S. Ouaro
We study well-posedness of triply nonlinear degenerate elliptic-parabolic-hyperbolic problems of the kind
b(u)t−div𝔞̃ (u,∇φ(u))+ψ(u)=f,u|t=0=u0
in a bounded domain with homogeneous Dirichlet boundary conditions. The nonlinearities b,φ and ψ are supposed to be continuous non-decreasing, and the nonlinearity 𝔞̃ falls within the Leray-Lions(...)
degenerate elliptic-hyperbolic-parabolic equation; Leray-Lions type operator; homogeneous Dirichlet problem; entropy solution; well-posedness; continuous dependence on data
ARTICLE
Weak solutions for anisotropic nonlinear elliptic equations with variable exponents
B. Koné, S. Ouaro, S. Traoré
We study the anisotropic boundary-value problem
−∑i=1N∂∂xiai(x,∂∂xiu)=fin Ω,u=0on ∂Ω,
where Ω is a smooth bounded domain in ℝN (N≥3). We obtain the existence and uniqueness of a weak energy solution for f∈L∞(Ω), and the existence of weak energy solution for general data f dependent on u.
ev spaces; weak energy solution; variable exponents; electrorheological fluids
ARTICLE
Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach Spaces
Khalil Ezzinbi, Hamidou Toure, Issa Zabsonre
In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense of Grimmer [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transactions of the Am(...)
Mots clés non renseignés
ARTICLE
Weak and entropy solutions to nonlinear elliptic problems with variable exponent.
S. Ouaro, S. Traoré
The authors study nonlinear boundary value problem with the nonlinear operator of p-Laplacian-type and Dirichlet boundary condition. The authors obtain two existence results: in first a unique entropy solution is obtain and in the second a week solution is produced.
generalized Lebesgue-Sobolev spaces; weak energy solution; entropy solution; p(x)-Laplace operator; electrorheological fluids
ARTICLE
Uniqueness of entropy solutions of nonlinear elliptic-parabolic-hyperbolic problems in one dimension space.
S. Ouaro
We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form b(u)t−a(u,φ(u)x)x=f with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an L1-contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data.
entropy solution; L1-contraction principle; homogeneous Dirichlet conditions; initial conditions