Article | REF: AF190 V1

Partial differential equations

Authors: Claude BARDOS, Thierry PAUL

Publication date: October 10, 2010

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1. First-order equations

Reading guide

In Section 1, we present in detail the case of a PDE that directly generalizes Cauchy-Lipschitz theory. The case of Hamiltonian dynamics will also be present in several sections, as one of the red threads of our presentation.

Section 2 introduces the Schrödinger equation both for its own sake and because it has historically been a driving force behind the development of functional analysis.

Sections 3, 4 and 5 introduce the more classical, second-order elliptic and parabolic operators, with a view to dealing with significantly more macroscopic issues.

The wave equation, the subject of Section 1 of

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First-order equations