PDEs and Applications seminar: The surface diffusion flow with elasticity

  • Date: –12:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Vesa Julin, University of Jyväskylä
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

Abstract: I will discuss about short-time existence of a smooth solution to the surface diffusion equation with an elastic term. The equation models the evolution of material voids inside a stressed elastic

solid, but from mathematical point of view it can be regarded as canonical nonlocal perturbation of the surface diffusion by an additive elastic contribution. The elastic part is not, in general, lower order with respect to the area and therefore in the physical literature people often considers a regularized variant of the flow with  an additional curvature term. 

In our recent result we prove the short time existence without any additional curvature regularization. I will also discuss about the asymptotic stability of strictly stable stationary sets. This is a joint work with Nicola Fusco (Napoli) and Massimiliano Morini (Parma).