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arXiv · 1407.5557

The Cauchy problem for tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions

Pablo Alvarez-Caudevilla·Jonathan D. Evans·Victor A. Galaktionov
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Abstract

Fundamental global similarity solutions of the tenth-order thin film equation u_{t} = \nabla \cdot(|u|^{n} \n \D^4 u) in R^N \times R_+, where n>0 are studied. The main approach consists in passing to the limit n \to 0^+ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation u_t= \D^5 u in R^N \times \re_+.

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Pablo Alvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov. 2014-07-21. The Cauchy problem for tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions. https://arxiv.org/abs/1407.5557

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