Interior 'buckling' and non-uniqueness in a class of incompressible variational problems

Abstract: The talk is about a class variational problems whose associated energies $E_{\eps}$ can be thought of as perturbations of the Dirichlet energy. These energies have countably many pairs of planar, measure-preserving stationary points $u^n_{\pm}$ with the properties that (a) $E_{\eps}(u^n_+)=E_{\eps}(u^n_-)$ and (b) the maps $u^n_{\pm}$ cause `buckling' at the centre $0$ of the unit ball $B$ in $\mathbb{R}^2$ while acting as the identity on $\partial B$. Numerical calculations show that $n$ can be treated as a proxy for the `number of buckles' that occur at $0$, and that, as one might expect, $E_{\eps}(u^n_{\pm})$ increases as $n$ does. This is joint work with J. Deane.

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).