Last modified on 17 August 2014, at 21:15

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 ContentsEdit

Introduction and first examples

Linear partial differential equationsEdit

Using elementary analysisEdit

Transport equation

Using distributionsEdit

Test function spaces

Distributions

Fundamental Solutions, Green's functions, Green's kernels and Dirichlet Problems

Poisson's equation

Heat equation

Helmholtz' equation

Using the Fourier transformEdit

The Fourier transform

Wave equation

Nonlinear partial differential equationsEdit

Using the characteristic equationsEdit

The characteristic equations

Using calculus of variationsEdit

Sobolev spaces

Calculus of variations

Using monotone operatorsEdit

Monotone operators

AppendixEdit

The Malgrange-Ehrenpreis theorem

Answers to the exercises