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Kato inequalities for scalar hyperbolic and degenerate parabolic problems

  • Date June 12, 2015
  • Hour 12 pm
  • Room GSSI Main Lecture Hall
  • Speaker Boris Andreianov (Universite de Franche-Comte)

Uniqueness and stability of solutions for a large family of scalar convection-diffusion problems  are deduced from the Kato inequality, which expresses localized L^1 contraction and order-preservation properties.  E.g. in the case of the scalar hyperbolic conservation law, the Kruzhkov definition of entropy solution can be seen as a particular family of Kato inequalities.

We will discuss how Kato inequalities can be obtained and how they can be exploited in the well-posedness theory, including boundary-value problems and interface coupling problems.