Santiago Betelú

Capillarity driven spreading of power-law fluids

Abstract We investigate the spreading of thin liquid films of power-law rheology. We construct an explicit travelling wave solution and source-type similarity solutions. We show that when the nonlinearity exponent λ for the rheology is larger than one, the governing dimensionless equation h t + ( h λ +2 | h xxx | λ −1 h xxx ) x =0 admits solutions with compact support and moving fronts. We also show that the solutions have bounded energy dissipation rate.

Explicit stationary solutions in multiple well dynamics and non-uniqueness of interfacial energy densities

We present a theory that enables us to construct heteroclinic connections in closed form for

Singularities on charged viscous droplets

2\bf{u}_{xx}=W_{\bf u}({\bf u})

Capillarity driven spreading of circular drops of shear-thinning fluid

, where

Area-Based Medial Axis of Planar Curves

x\in\mathbb{R},\;{\bf u}(x)\in \mathbb{R}^2

Fingering from Ionization Fronts in Plasmas

and

Affine invariant erosion of 3D shapes

W

Instantaneous viscous flow in a corner bounded by free surfaces

is a smooth potential with multiple global minima. In particular, multiple connections between global minima are constructed for a class of potentials. With these potentials, numerical simulations for the vector Allen-Cahn equation

Noise-Resistant Affine Skeletons of Planar Curves

{\bf u}_t= 2\epsilon^2 \Delta {\bf u}-W_{\bf u}({\bf u})

A two-dimensional similarity solution for capillary driven flows

in two space dimensions with small