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arXiv · 1411.6142

Gibbs phenomenon for dispersive PDEs on the line

Gino Biondini·Thomas Trogdon
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Abstract

We investigate the Cauchy problem for linear, constant-coefficient evolution PDEs on the real line with discontinuous initial conditions (ICs) in the small-time limit. The small-time behavior of the solution near discontinuities is expressed in terms of universal, computable special functions. We show that the leading-order behavior of the solution of dispersive PDEs near a discontinuity of the ICs is characterized by Gibbs-type oscillations and gives exactly the Wilbraham-Gibbs constant.

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Gino Biondini, Thomas Trogdon. 2014-11-22. Gibbs phenomenon for dispersive PDEs on the line. https://arxiv.org/abs/1411.6142

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