### Abstract

As a key example, the sixth-order doubly degenerate parabolic equation from thin film theory,

u(t) = (vertical bar u vertical bar(m)vertical bar u(xxxxx)vertical bar(n)u(xxxxx))(x) in R x R+,

with two parameters, n >= 0 and m is an element of (-n, n + 2), is considered. In this first part of the research, various local properties of its particular travelling wave and source-type solutions are studied. Most complete analytic results on oscillatory structures of these solutions of changing sign are obtained for m = 1 by an algebraic-geometric approach, with extension by continuity for m approximate to 1.

Original language | English |
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Pages (from-to) | 4030-4048 |

Number of pages | 19 |

Journal | Nonlinear Analysis: Theory Methods & Applications |

Volume | 72 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Jun 2010 |

### Keywords

- oscillatory behaviour
- thin film equations
- nonlinear dispersion and wave equations
- interfaces
- source-type solutions
- the Cauchy problem

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## Cite this

Chaves, M., & Galaktionov, V. A. (2010). On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties.

*Nonlinear Analysis: Theory Methods & Applications*,*72*(11), 4030-4048. https://doi.org/10.1016/j.na.2010.01.034