2020 Atlanta USA

Hypocoercivity in evolutionary PDEs

Anton Arnold
Vienna University of Technology
Eric Carlen
Rutgers university
Arnaud Guillin
Clermont-Auvergne University
  The term "hypocoercivity" was coined by C.Villani for describing the large-time convergence to equilibrium for certain degenerate, dissipative evolution equations. Initially the focus was on kinetic PDEs of Fokker-Planck or Boltzmann-type, but the methods were later found to apply to a wider range of equations, including reaction-diffusion or reaction-transport systems (binary collisions in mixtures, chemical reactions). In such models, "hypocoercivity" refers to the exponential convergence to the steady state, resulting from an interplay between a degenerately dissipative component of the evolution machanism, and a conservative (often Hamiltonian) part of the evolution mechanism. The last decade has seen an ever growing interest in the development of hypocoercivity. A large part of this progess is based on modifications of the classical Bakry-Emery approach, which was developed to prove exponential decay towards equilibrium for a large class of nondegenerate dissipative PDEs. This approach is based on analyzing appropriate Lyapunov functionals that can often be interpreted as relative entropy or free energy. Hypocoercivity techniques typically aim at modifying such Lyapunov functionals, to still obtain exponential decay - even for degenerate problems. This workshop will bring together many of the leading researchers is this field, with background in classical PDE analysis, kinetic equations, and probability.