Global existence and stability for dissipative processes coupled across volume and surface

Abstract: The modelling of technological and biological processes and devices is often characterized by non-smoothness: material edges and corners, abruptly changing material properties and a large scope of relevant temporal and spatial scales. From a PDE point-of-view, we need to deal with domains of low boundary regularity, mixed and dynamic boundary conditions, degeneracy and discontinuity of parameters, and, possibly after rescaling, with the coupling of dynamics across voulme and lower-dimensional interfaces or surfaces.

In this talk, I want to consider models of non-linear reaction-drift-diffusion type in non-smooth and/or volume-surface settings and discuss their analysis based on the choice of specific functional analytic settings. The aim is to discuss some aspects of the interaction of thermodynamically consistent modelling and the analysis of the PDE and to establish strategies for simultaneously dealing with non-linearity and non-smoothness.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).