Partial Differential Equations

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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.

Table of Contents[edit]

Introduction and first examples

Linear partial differential equations[edit]

Using distributions[edit]

Distributions

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

Poisson's equation

Heat equation

Transport equation

Wave equation

Using the Fourier transform[edit]

The Fourier transform

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 Banach-Steinhaus theorem for locally convex sets

The Malgrange-Ehrenpreis theorem