Partial Differential Equations

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This Wikibook is UNDER CONSTRUCTION! It will hopefully be completed in the months August and September of 2014.

Partial differential equations are equations which describe several 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

Linear partial differential equations[edit]

Using elementary analysis[edit]

Transport equation

Using distributions[edit]

Test function spaces

Distributions

Fundamental solutions, Green's functions and Green's kernels

Poisson's equation

Heat equation

Helmholtz' equation

Using the Fourier transform[edit]

The Fourier transform

Wave equation

Nonlinear partial differential equations[edit]

Using the characteristic equations[edit]

The characteristic equations

Using calculus of variations[edit]

Sobolev spaces

Calculus of variations

Using monotone operators[edit]

Monotone operators

Appendix[edit]

The Malgrange-Ehrenpreis theorem

Answers to the exercises