Speaker
Description
In recent years, interface models have become increasingly popular in mathematical biology for describing tumour growth. Among these, the Cahn–Hilliard–Biot model was the first to incorporate both mechanical stress and fluid flow through a heterogeneous, saturated porous medium. In subsequent works, the original model was further extended to include Kelvin–Voigt viscoelasticity. Since the Cahn–Hilliard–Biot system is a diffuse-interface model, it is natural to ask about related sharp-interface systems.
Motivated by this question, we introduce a novel viscoelastic Mullins–Sekerka system with second-gradient terms and a constant contact angle at the boundary, which we derive as an H⁻¹-H¹-type gradient flow of the perimeter and an elastic energy. Moreover, we discuss different notions of weak solutions, namely BV solutions and varifold solutions satisfying an optimal energy dissipation principle in the spirit of De Giorgi.
This is joint work with Helmut Abels and Harald Garcke (Universität Regensburg)