Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I
arXiv:0902.1425
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.
41 pages, 27 figures
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Cited by in corpus (9)
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- Towards the KPP-Problem and log t-Front shift for Higher-Order Nonlinear PDEs II. Quasilinear Bi- and Tri-Harmonic Equations
- Schock waves and compactons for fifth-order nonlinear dispersion equations. II
- Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations
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- Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation
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- Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range II. Higher-order diffusion
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