# math.AP

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

### Matter field from diffeomorphism: on a theme of Capoferri and Vassiliev

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

### Oscillatory Solutions to the Heat Equation

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 and Wave Maps

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

### Convergence to Planewaves for Solutions to Schrödinger's equation III

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

### Convergence to Planewaves for Solutions to Schrödinger's equation II

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

### Convergence to Planewaves for Solutions to Schrödinger's equation

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

### Simulating Closed Cosmic Strings

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

### Shooting particles with Python

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

### Blow-up of QNLW with Small Initial Data à la Christodoulou

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

### Notes on Sobolev Spaces

Lecture notes introducing Sobolev spaces.