Airy equation: Difference between revisions

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Revision as of 23:41, 10 April 2007

The (homogeneous) Airy equation is given by

It is the linear component of many equations of KdV type, including of course the Korteweg-de Vries equation itself. For applications to such nonlinear perturbations of the homogeneous Airy equation, it is often important to study the more general inhomogeneous Airy equation

for various forcing terms F. Of course, the inhomogeneous and homogeneous equations are related by Duhamel's formula.

A large number of linear, bilinear, trilinear, and multilinear estimates for this equation are known; see the page on Airy estimates for more details.