zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stability of liquid film falling down a vertical non-uniformly heated wall. (English) Zbl 1149.76024
Summary: We study the stability of a viscous film flowing down a vertical non-uniformly heated wall under gravity. The wall temperature is assumed linearly distributed along the wall, and the free surface is taken to be adiabatic. A long wave perturbation method is used to derive the nonlinear evolution equation for the falling film. Using the method of multiple scale, the nonlinear stability analysis is performed for travelling wave solution of the evolution equation. The complex Ginzburg-Landau equation is determined to discuss the bifurcation analysis of the evolution equation. The results indicate that the supercritical unstable region increases and the subcritical stable region decreases with the increase in Peclet number. It has been also shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region.
76E17Interfacial stability and instability (fluid dynamics)
76E30Nonlinear effects (fluid mechanics)
76A20Thin fluid films (fluid mechanics)