# Partial Differential Equations

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This Wikibook is UNDER CONSTRUCTION! It will hopefully be completed in the not too distant future.

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]

- Introduction and first examples
- Transport equation
- Test functions
- Distributions
- Fundamental solutions, Green's functions and Green's kernels
- Poisson's equation
- Heat equation
- The Fourier transform
- Wave equation
- The Malgrange-Ehrenpreis theorem
- Characteristic equations
- Sobolev spaces
- Convex things
- Calculus of variations
- Bochner's Integral
- Monotone operators
- Answers to the exercises
- Appendix I: The uniform boundedness principle for (tempered) distributions