On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties
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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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.
|Creators||Chaves, M.and Galaktionov, V. A.|
|Uncontrolled Keywords||oscillatory behaviour,thin film equations,nonlinear dispersion and wave equations,interfaces,source-type solutions,the cauchy problem|
|Departments||Faculty of Science > Mathematical Sciences|
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