Narrow Results

In the first part of this paper, we derive an infinite-dimensional partial differential equation which describes an economic equilibrium in a model of storage which includes an infinite number of non-atomic agents. This equation has the form of a mean field game master equation. The second part of the paper is devoted to the mathematical study of the Hamilton–Jacobi–Bellman equation from which the previous equation derives. This last equation is both singular and set on a Hilbert space and thus raises new mathematical difficulties.

We briefly review the derivation due to Alvarez, Guichard, Morel and the author of mathematical models in Image Processing. We deduce from classical axions in Computer Vision some nonlinear partial differential equations of evolution type that correspond to general multi-scale analysis (scale-space). We also obtain specific nonlinear models that satisfy additional invariances which are relevant for the analysis of images.

The following sections are included:

• ETUDES

• ACTIVITIES PROFESSIONNELLES

• DISTINCTIONS

• RESPONSABILITIES COLLECTIVES
  • Responsabilités administratives
  • Comité de rédaction de “séries”
  • Membre des comités de rédaction de:
  • Organisateur de colloques
  • Comités scientifiques
  • Comités de prix

• ENCADREMENT

The following sections are included:

• Introduction

• Boltzmann Equation
  • Existence and compactness results
  • Velocity averaging
  • Gain terms and Radon transforms

• Compressible Euler and Navier-Stokes Equations
  • 1D isentropic gas dynamics
  • Compensated compactness and Hardy spaces
  • Isentropic Navier–Stokes equations

• Perspectives, Trends, Problems and Methods

• References