### authors

- ALVAREZ CAUDEVILLA, PABLO
- EVANS, J. D.
- GALAKTIONOV, V. A.

- March 2015

- 807

- 827

- 3

- 35

- 1078-0947

- 1553-5231

- Aparece tambien en Arxiv.com : arXiv:1407.5554v1 Abstract: Fundamental global similarity solutions of the standard form u gamma(x,t) = t(-alpha)gamma(f gamma)(y), with the rescaled variable y = x/t(beta gamma), beta(gamma) = 1 n alpha gamma/10, where alpha gamma > 0 are real nonlinear evenvalues (gamma is a multiindex in R-N) of the tenth-order thin film equation (TFE-10) u(t) = del . (vertical bar u vertical bar(n) del Delta(4)u) in R-N x R+, n > 0, (0.1) (0, 1) are studied. The present paper continues the study began in [1]. Thus, the following questions are also under scrutiny: (I) Further study of the limit n -> 0, where the behaviour of finite interfaces and solutions as y > infinity are described. In particular, for N = 1, the interfaces are shown to diverge as follows: vertical bar x(0)(t)vertical bar similar to 10 (1/n sec (4 pi/9)) (9/10) t(1/10) -> infinity as n -> 0+. (II) For a fixed n is an element of (0, 9/8), oscillatory structures of solutions near interfaces. (III) Again, for a fioxed n is an element of (0, 9/8), global structures of some nonlinear and analytical methods

- Mathematics

- thin film equation; the cauchy problem; source-type global similarity solutions of changing sign; parabolic equations