# Partial Differential Equations

From Wikibooks, open books for an open world

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 Contents[edit]

### Linear partial differential equations[edit]

- 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 equations[edit]

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