Publications (392)
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
ARTICLE
Existence and regularity of solutions for some partial functional integrodifferential equations 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 in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathemati(...)
Mots clés non renseignés
ARTICLE
Entropy solutions to the obstacle problem for nonlinear elliptic problems with variable exponent and L1-data.
S. Ouaro, S. Traoré
We establish for L1-data, existence, uniqueness and continuous dependence results to the obstacle problem for nonlinear elliptic equations with variable exponent, where the variable exponent is supposed only measurable. Other classical results about stability properties of the corresponding coincidence set and the Lewy-Stampacchia inequalities(...)
obstacle problem; variable exponent; entropy solutions; weak energy solutions; coincidence set; Lewy-Stampacchia inequalities
ARTICLE
Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems.
S. Ouaro, H. Touré
We study the Cauchy problem associated with the nonlinear elliptic-parabolic equation
b(u)t−a(u,φ(u)x)x=f.
We prove an L1-contraction principle and hence the uniqueness of entropy solutions, under rather general assumptions on the data.
Elliptic; parabolic; degenerate; weak solution; entropy solution; L1-contraction principle
ARTICLE
Entropy solutions of nonlinear elliptic-parabolic-hyperbolic degenerate problems in one dimension.
S. Ouaro
If I is an open bounded interval and T>0, the initial-boundary-value problem
(EP)⎧⎩⎨⎪⎪b(u)t−a(u,φ(u)x)x=fb(u)=v0u=0in Q=]0,T[×I,on {0}×Ion Γ=]0,T[×∂I
is under consideration, where a:(z,ξ)∈ℝ×ℝ→ℝ is continuous, nondecreasing in ξ∈ℝ with a(0,0)=0; b:ℝ→ℝ is continuous, nondecreasing and surjective with b(0)=0; and φ:ℝ→ℝ is continuous, nondecre(...)
initial-boundary-value problem; homogeneous Dirichlet conditions
ARTICLE
Continuous dependence of solutions to nonlinear elliptic-parabolic-hyperbolic problem in one dimension
S. Ouaro, B. K. Bonzi
We consider a nonlinear elliptic-parabolic-hyperbolic equation of the form:
b(u)t−a(u,φ(u)x)x=f.
We show the continuous dependence of the “mild solution” of the associated Cauchy problem with respect to the data a, f and v0 without Alt and Luckhaus structure condition.
Cauchy problem
ARTICLE
Entropy solutions of a stationary problem associated to a nonlinear parabolic strongly degenerate problem in one space dimension.
S. Ouaro
We study a nonlinear elliptic degenerate equation with the form: b(u)−a(u,φ(u)x)x=f which is associated to the elliptic-parabolic-hyperbolic equation of the form: b(u)t−a(u,φ(u)x)x=f. We prove in this work without Alt and Luckhaus structure condition existence and uniqueness of entropy solutions of the associated Dirichlet problem. We also def(...)
elliptic; parabolic; hyperbolic; weak solution; entropy solution
ARTICLE
On some nonlinear elliptic-parabolic equations of second order
S. Ouaro, H. Touré
We study a nonlinear elliptic-parabolic PDE in one-dimensional space with the form: b(u)t−a(u,φ(u)x)x=f. Using the nonlinear semigroups theory in Banach spaces, we establish existence and uniqueness of mild solutions of the associated Cauchy problem under general assumptions on the data. We prove under additional assumptions, that mild solutio(...)
one space dimension; nonlinear semigroups; mild solutions
ARTICLE
Sur un problème de type elliptique parabolique non linéaire
S. Ouaro, H. Touré
We study the general equation b(u)t=a(u,φ(u)x)x+f of elliptic-parabolic type. Using the theory of evolution equation governed by an accretive operator, we establish existence and uniqueness of mild solutions to the associate Cauchy problem, under general assumptions on the data. With an additional structural condition of Alt-Luckhauss type, we(...)
mild solutions; Cauchy problem; structural condition of Alt-Luckhauss type; weak solutions
ARTICLE
Etude d’une équation elliptique associée à un problème parabolique-elliptique non linéaire
S. Ouaro, H. Touré
We study the general equation b(u)−a(u,φ(u)x)x=f of second order elliptic type, which may degenerate onto a first order equation for some value of u. We introduce for that a notion of entropy type solution for the elliptic problem. We define an L1 operator associated to the equation. We show that the operator is accretive in L1, with dense dom(...)
elliptic equation; weak solution; entropy solution; accretive operator