Publications (392)
ARTICLE
Existence and uniqueness of weak and entropy solutions for homogeneous Neumann boundary-value problems involving variable exponents
B.K. Bonzi, I. Nyanquini, S. Ouaro
We study the nonlinear homogeneous Neumann boundary-value problem
b(u)−diva(x,∇u)=fin Ωa(x,∇u).η=0on ∂Ω,
where Ω is a smooth bounded open domain in ℝN, N≥3 and η the outer unit normal vector on ∂Ω. We prove the existence and uniqueness of a weak solution for f∈L∞(Ω) and the existence and uniqueness of an entropy solution for L1-data f. The f(...)
elliptic equation; weak solution; entropy solution; Leray-lions operator; variable exponent
ARTICLE
The multiplicative anomaly for determinants revisited; locality
Marie Françoise Ouedraogo, Sylvie Paycha
Observing that the logarithm of a product of two elliptic operators differs from the sum of the logarithms by a finite sum of operator brackets, we infer that regularised traces of this difference are local as finite sums of noncommutative residues. From an explicit local formula for such regularised traces, we derive an explicit local formula(...)
pseudodifferential operators, noncommutative residue, canonical and weighted traces, zeta and weighted determinants
ARTICLE
Weak and entropy solutions to nonlinear Neumann boundary-value problems with variable exponents
Stanislas Ouaro and Safimba Soma
In this article, we study the following nonlinear Neumann boundary-value problem diva(x,ru)þjujp(x)2 u1⁄4f in , @u 1⁄4 0 on @, where is a
@
smooth bounded open domain in RN, N 3, @u is the outer unit normal @
derivative on @, div a(x, ru) a p(x)-Laplace type operator. We prove the existence and uniqueness of a weak solution for(...)
generalized Lebesgue and Sobolev spaces, weak solution, entropy solution, p(x)-Laplace operator
ARTICLE
On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian
A. Guiro, I. Nyanquini, S. Ouaro
The solvability of Neumann discrete boundary value problem involving anisotropic exponents is discussed in the paper. They apply variational methods, using a minimization theorem.
discrete boundary value problem; critical point; weak solution; electrorheological fluids
ARTICLE
Uniqueness of traces on log-polyhomogeneous pseudodifferential operators
Catherine Ducourtioux, Marie Françoise Ouedraogo
We show how to derive the uniqueness of graded or ordinary traces on some algebras of log-
polyhomogeneous pseudodifferential operators from the uniqueness of their restriction to classical
pseudodifferential ones
log-polyhomogeneous pseudodifferential operators
ARTICLE
Periodic solutions in the α-norm for some partial functional differential equations with finite delay.
K. Ezzinbi, B.A. Kyelem, S. Ouaro
The paper deals with the partial functional differential equation with finite delay in the α-norm
dudt(t)=−Au(t)+f(t,ut),t∈ℝ,
where f:ℝ×Cα→X is a continuous function, σ-periodic in the first argument, A:D(A)⊂X→X is a linear operator, −A is the infinitesimal generator of an analytic semigroup of linear operators (T(t))t≥0 on a Banach space X,(...)
analytic semigroup; partial functional differential equations; α-norm; multivalued maps; periodic solution; Horn’s fixed point theorem
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