# Partial Differential Equations

Some partial differential equations describe important processes in nature. This wikibook shows how to solve different kinds of partial differential equations and/or gives existence and uniqueness results, using a variety of methods.

Authors should be aware of the stylistic guidelines.

## Table of ContentsEdit

### Linear partial differential equationsEdit

- The transport equation
- Test functions
- Distributions
- Fundamental solutions, Green's functions and Green's kernels
- The heat equation
- Poisson's equation
- The Fourier transform
- The wave equation
- The Malgrange-Ehrenpreis theorem

### Nonlinear partial differential equationsEdit

- The characteristic equations
- Sobolev spaces
- Convex analysis
- Calculus of variations
- Bochner's Integral
- Monotone operators