The Cauchy Problem for a Tenth-Order Thin Film Equation I. Bifurcation of Oscillatory Fundamental Solutions |
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Authors: | Pablo Álvarez-Caudevilla Jonathan D Evans Victor A Galaktionov |
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Institution: | 1. Universidad Carlos III de Madrid, Av. Universidad 30, 28911, Legans, Madrid, Spain 2. Department of Mathematical Science, Claverton Down, University of Bath, Bath, BA2 7AY, UK
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Abstract: | Fundamental global similarity solutions of the tenth-order thin film equation $$u_{t} = \nabla . (|u|^{n} \nabla \Delta^{4}u) \,\,\,\, {\rm in} \,\,\,\, \mathbb{R}^{N} \times \mathbb{R}_{+}$$ , where n > 0 are studied. The main approach consists in passing to the limit ${n \rightarrow 0^{+}}$ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation $$u_{t} = \Delta^{5}u \,\,\,\, {\rm in} \,\,\,\, \mathbb{R}^{N} \times \mathbb{R}_{+}$$ . |
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