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On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties


Reference:

Chaves, M. and 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), pp. 4030-4048.

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http://dx.doi.org/10.1016/j.na.2010.01.034

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.

Details

Item Type Articles
CreatorsChaves, M.and Galaktionov, V. A.
DOI10.1016/j.na.2010.01.034
Uncontrolled Keywordsoscillatory behaviour, thin film equations, nonlinear dispersion and wave equations, interfaces, source-type solutions, the cauchy problem
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code18933

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