This is an arXiv category tag for the analysis of partial differential equations.

This is an arXiv category tag for the analysis of partial differential equations.

I try to reformulate an idea of Capoferri and Vassiliev in the infinitesimal limit and see where it goes.

As we all learned in a first course in PDEs, for "reasonable" initial data $u_0$, the solution to the linear heat equation …

The "Nirenberg trick" or "Nirenberg transformation" is the observation1 that the semilinear wave equation …

In this installment, we look at Schrödinger's equation with barriers, and study the decay of the solutions.

We use Laplace transform arguments to look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation …

We look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation to plane waves.

One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …

Numpy simulation of how classical and quantum particles interact with potential barriers.

Lecture slides that Gustav Holzegel and I used for the January 13-14, 2014 OXPDE Workshop at Oxford University.

Lecture notes introducing Sobolev spaces.