# Partial Differential Equations

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This wikibook aims at explaining how to solve partial differential equations, and if that's not possible, how to at least obtain some uniqueness and existence results.

## Contents

## Table of contents[edit]

- Introduction
- Transformation of variables
- Method of characteristics
- Calculus of variations
- Fourier-analytic methods (requires Fourier analysis)
- The wave equation (requires integration on manifolds)
- Fundamental solutions (requires distribution theory)
- Poisson's equation (requires integration on manyfolds and harmonic function theory)
- The heat equation
- Sobolev spaces (requires some functional analysis)
- Monotone operators (requires convex analysis)

## Old table of Contents[edit]

Authors should be aware of the stylistic guidelines.

### 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