The Cauchy Problem for a Tenth-Order Thin Film Equation I. Bifurcation of Oscillatory Fundamental Solutions

@article{lvarezCaudevilla2013TheCP,
  title={The Cauchy Problem for a Tenth-Order Thin Film Equation I. Bifurcation of Oscillatory Fundamental Solutions},
  author={Pablo {\'A}lvarez-Caudevilla and Jonathan D. Evans and Victor A. Galaktionov},
  journal={Mediterranean Journal of Mathematics},
  year={2013},
  volume={10},
  pages={1761-1792}
}
AbstractFundamental 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}_… CONTINUE READING
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