Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I
Analysis of PDEs
2009-02-10 v1
Abstract
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational techniques give countable families of various compactly supported solutions with oscllatory behaviour cloase to the interfaces. Overall, the whole set of such compact patterns reveals certain chaotic properties and contains solutions of arbitrary complexity.
Cite
@article{arxiv.0902.1425,
title = {Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I},
author = {V. A. Galaktionov and E. Mitidieri and S. I. Pohozaev},
journal= {arXiv preprint arXiv:0902.1425},
year = {2009}
}
Comments
41 pages, 27 figures