Initial Value Problems in Lp for Systems with Variable Coefficients.
Initial-boundary value problem with a nonlocal condition for a viscosity equation.
Interaction contrôlée dans les équations aux dérivées partielles non linéaires
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
We construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier–Lebesgue space with and scaling like , for small . We also show the invariance of this measure.
Inverse problems for the volume potential
La première valeur propre du laplacien pour le problème de Dirichlet
Large data local solutions for the derivative NLS equation
We consider the derivative NLS equation with general quadratic nonlinearities. In [2] the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension . Here we prove a similar result for large initial data in all dimensions .
Le problème de Cauchy et la propagation des singularités pour une classe des systèmes hyperboliques non symétrisables
Le problème mixte hyperbolique
Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems.
Local exact lagrangian controllability of the Burgers viscous equation
Local Existence of Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.
Localized minimizers of flat rotating gravitational systems
Longtime behavior of semilinear reaction-diffusion equations on the whole space
Low regularity Cauchy theory for the water-waves problem: canals and swimming pools
The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [1, 2], after suitable para-linearizations, the system can be arranged into...
Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system.
Mathematical modelling of rock bolt systems. I
The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.
Mathematical modelling of rock bolt systems. II
The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied.
Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys
In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.
Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow
Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and -maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented...