An improved regularity criteria for the MHD system based on two components of the solution
As observed by Yamazaki, the third component of the magnetic field can be estimated by the corresponding component of the velocity field in
An inhomogeneous Dirichlet problem for a non-hypoelliptic linear partial differential operator.
Analytic semigroups generated on a functional extrapolation space by variational elliptic equations
We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space consinsting of all derivatives of hölder-continuous functions in where is a domain in not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space . We prove also that the spaces can be considered as extrapolation spaces relative to suitable non-variational operators....
Analytic solutions for the classical two-phase Stefan problem
Analyticité des solutions des équations de Vlassov-Poisson
Analyticité locale pour les solutions de l'équation d'Euler
Analyticité microlocale et itères d'opérateurs
Analyticity and smoothing effect for the Schrödinger equation
Analyticity for some degenerate one-dimensional evolution equations
We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Approximation de la solution de viscosité d'un problème d'Hamilton-Jacobi.
Approximation of the viscosity solution of a Hamilton-Jacobi problem.
In this paper, a mathematical analysis of in-situ biorestoration is presented. Mathematical formulation of such process leads to a system of non-linear partial differential equations coupled with ordinary differential equations. First, we introduce a notion of weak solution then we prove the existence of at least one such a solution by a linearization technique used in Fabrie and Langlais (1992). Positivity and uniform bound for the substrates concentration is derived from the maximum principle...
Approximations of Sobolev maps between an open set and an Euclidean sphere, boundary data, and singularities.
Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.
Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem
Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary.
Asymptotic solutions to Fuchsian equations in several variables
The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.
Asymptotics of solutions to the Dirichlet-Cauchy problem for parabolic equations in domains with edges
This paper is concerned with the Dirichlet-Cauchy problem for second order parabolic equations in domains with edges. The asymptotic behaviour of the solution near the edge is studied.