TY - JOUR

T1 - On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties

AU - Chaves, M

AU - Galaktionov, Victor A

PY - 2010/6/1

Y1 - 2010/6/1

N2 - 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.

AB - 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.

KW - oscillatory behaviour

KW - thin film equations

KW - nonlinear dispersion and wave equations

KW - interfaces

KW - source-type solutions

KW - the Cauchy problem

UR - http://www.scopus.com/inward/record.url?scp=77949488245&partnerID=8YFLogxK

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

U2 - 10.1016/j.na.2010.01.034

DO - 10.1016/j.na.2010.01.034

M3 - Article

VL - 72

SP - 4030

EP - 4048

JO - Nonlinear Analysis: Theory Methods & Applications

JF - Nonlinear Analysis: Theory Methods & Applications

SN - 0362-546X

IS - 11

ER -