In this paper, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which called reaction–interface systems. All weak entire solutions originating finitely many excited intervals completely characterized. For infinitely intervals, periodic wave trains and time-periodic discussed. In particular, we study dispersion rel...

This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional incompressible Navier-Stokes equations and to show how they relate to LES (ii) to introduce...

Standard weak solutions to the Poisson problem on a bounded domain have squareintegrable derivatives, which limits the admissible regularity of inhomogeneous data. The concept of solution may be further weakened in order to define solutions when data is rough, such as for inhomogeneous Dirichlet data that is only square-integrable over the boundary. Such very weak solutions satisfy a nonstandar...