Singularités isotropes des solutions d'équations elliptiques non linéaires
Sobolev solution for semilinear PDE with obstacle under monotonicity condition.
Soliton solutions for quasilinear Schrödinger equation with critical exponential growth in
In this work, we study the existence of nonnegative and nontrivial solutions for the quasilinear Schrödinger equation where is the -Laplacian operator, is continuous and behaves as when . Using the Nehari manifold method and the Schwarz symmetrization with some special techniques, the existence of a nonnegative and nontrivial solution with as is established.
Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier
2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.We give here examples of equations of type (1) ∂tt2 y -p(t, Dx) y = 0, where p is a singular pseudo-differential operator with regular global solutions when the Cauchy data are regular, t ∈ R, x ∈ R5.
Solutions of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents
Some solutions are obtained for a class of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents by variational methods and some analysis techniques.
Solvability of a class of phase field systems related to a sliding mode control problem
We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
Solvability of the Poisson equation in weighted Sobolev spaces
The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations
This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Some results of nontrivial solutions for a nonlinear PDE in Sobolev space.
Some results on strongly nonlinear anisotropic differential equations
The paper concerns the existence of weak solutions to nonlinear elliptic equations of the form A(u) + g(x,u,∇u) = f, where A is an operator from an appropriate anisotropic function space to its dual and the right hand side term is in with 0 < m < 1. We assume a sign condition on the nonlinear term g, but no growth restrictions on u.
Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems
This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.
Strengthening upper bound for the number of critical levels of nonlinear functionals
Strong maximum principle for weak solutions of nonlinear parabolic differential inequalities
Sui problemi al contorno per sistemi di equazioni differenziali lineari del tipo di stabilità dell'equilibrio elastico
Sur la méthode variationnelle pour les équations aux dérivées partielles non linéaires du type elliptique; l'existence et la régularité des solutions
Sur la régularité des solutions faibles des équations elliptiques non linéaires
Sur la théorie globale des équations de Navier-Stokes compressible
Le but de cet article est de présenter quelques résultats mathématiques plus ou moins récents sur la théorie de l’existence globale en temps (solutions faibles et solutions fortes) pour les équations de Navier-Stokes compressibles en dimension supérieure ou égale à deux sans aucune hypothèse de symétrie sur le domaine et sans aucune hypothèse sur la taille des données initiales.
Sur l’appartenance dans la classe des solutions variationnelles des équations elliptiques non-linéaires de l’ordre en deux dimensions (Communication préalable)
Sur l'existence de la solution classique du problème de Poisson pour les domaines plans
Sur une méthode pour résoudre les équations aux dérivées partielles du type elliptique, voisine de la variationnelle