### Abstract

Fundamental global similarity solutions of the tenth-order thin film equation

*u _{t}*=∇.(|

*u*|

*∇Δ*

^{n}^{4}

*u*) in R

*×*

^{N}_{+}, where

*n*> 0 are studied. The main approach consists in passing to the limit

*n*→0

^{+}by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation

*u*=Δ

_{t}^{5}

*u*in R

_{t}*×R*

^{N}_{+ }.

Language | English |
---|---|

Pages | 1761-1792 |

Journal | Mediterranean Journal of Mathematics |

Volume | 10 |

Issue number | 4 |

DOIs | |

Status | Published - Nov 2013 |

### Fingerprint

### Cite this

**The Cauchy problem for a tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions.** / Álvarez-Caudevilla, Pablo; Evans, Jonathan D.; Galaktionov, Victor A.

Research output: Contribution to journal › Article

*Mediterranean Journal of Mathematics*, vol. 10, no. 4, pp. 1761-1792. https://doi.org/10.1007/s00009-013-0263-3

}

TY - JOUR

T1 - The Cauchy problem for a tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions

AU - Álvarez-Caudevilla, Pablo

AU - Evans, Jonathan D.

AU - Galaktionov, Victor A.

PY - 2013/11

Y1 - 2013/11

N2 - Fundamental global similarity solutions of the tenth-order thin film equation ut=∇.(|u|n∇Δ4u) in RN ×+, where n > 0 are studied. The main approach consists in passing to the limit n→0+ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation ut =Δ5ut in RN ×R+ .

AB - Fundamental global similarity solutions of the tenth-order thin film equation ut=∇.(|u|n∇Δ4u) in RN ×+, where n > 0 are studied. The main approach consists in passing to the limit n→0+ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation ut =Δ5ut in RN ×R+ .

UR - http://www.scopus.com/inward/record.url?scp=84874148604&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/s00009-013-0263-3

U2 - 10.1007/s00009-013-0263-3

DO - 10.1007/s00009-013-0263-3

M3 - Article

VL - 10

SP - 1761

EP - 1792

JO - Mediterranean Journal of Mathematics

T2 - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 4

ER -