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Résultats d’existence dans des espaces critiques pour le système de la MHD inhomogène

Hammadi Abidi, Taoufik Hmidi (2007)

Annales mathématiques Blaise Pascal

Nous démontrons dans cet article que le système MHD tridimensionnel à densité et viscosité variables est localement bien posé lorsque $({ρ_{0}}^{- 1} - 1, u_{0}, B_{0}) \in {\dot{B}}_{p 1}^{\frac{3}{p}} (ℝ^{3}) \times {\dot{B}}_{p 1}^{\frac{3}{p} - 1} (ℝ^{3}) \times {\dot{B}}_{p 1}^{\frac{3}{p} - 1} (ℝ^{3}),$ pour $p \in] 1, 3]$ et la densité initiale est proche d’une constante strictement positive. Nous démontrons également un résultat d’existence et d’unicité dans l’espace de Sobolev $H^{\frac{3}{2} + α} (ℝ^{3}) \times H^{\frac{3}{2} - 1 + α} (ℝ^{3}) \times H^{\frac{3}{2} - 1 + α} (ℝ^{3})$ pour $α > 0,$ sans aucune condition de petitesse sur la densité.

Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions.

Bouziani, Abdelfatah, Merazga, Nabil (2004)

Advances in Difference Equations [electronic only]

Scalings in homogenisation of reaction, diffusion and interfacial exchange in a two-phase medium

Peter, Malte A., Böhm, Michael (2007)

Proceedings of Equadiff 11

Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter $h \in Ω \subset ℝ^{m}$ . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.

Second-order boundary estimates for solutions to singular elliptic equations in borderline cases.

Anedda, Claudia, Porru, Giovanni (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Second-order estimates for boundary blowup solutions of special elliptic equations.

Anedda, Claudia, Buttu, Anna, Porru, Giovanni (2006)

Boundary Value Problems [electronic only]

Self-similar solutions for nonlinear Schrödinger equations.

Ye, Yaojun (2009)

Mathematical Problems in Engineering

Semilinear elliptic problems in unbounded domains

Aleksandra Orpel (2006)

Applicationes Mathematicae

We investigate the existence of positive solutions and their continuous dependence on functional parameters for a semilinear Dirichlet problem. We discuss the case when the domain is unbounded and the nonlinearity is smooth and convex on a certain interval only.