zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Instability of traveling waves of the convective-diffusive Cahn-Hilliard equation. (English) Zbl 1046.35098
Summary: We study the instability of the traveling waves of the convective--diffusive Cahn--Hilliard equation. We prove that it is nonlinearly unstable under $H^2$ perturbations, for some traveling wave solution that is asymptotic to a constant as $x \to \infty$.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35R25Improperly posed problems for PDE
WorldCat.org
Full Text: DOI
References:
[1] Novick-Cohen, A.; Segel, L. A.: Nonlinear aspects of the Cahn--Hilliard equation. Physica D 10, 277-298 (1984) · Zbl 0528.92004
[2] Cohen, D. S.; Murry, J. D.: A generalized diffusion model for growth and dispersal in a population. J. math. Biol. 12, 237-249 (1981) · Zbl 0474.92013
[3] Kwek KH. On the Cahn--Hilliard type equation. Doctoral thesis, Georgia Institute of Technology, 1991
[4] Liu, C.; Yin, J.: Convective--diffusive Cahn--Hilliard equation with concentration dependent mobility. Northeast. math. J. 19, No. 1, 86-94 (2003) · Zbl 1029.35139
[5] Strauss, W.; Wang, G.: Instability of traveling waves of the Kuramoto--Sivashinsky equation. Chin. ann. Math. B 23, No. 2, 267-276 (2002) · Zbl 1027.35013
[6] Goldstin, J. A.: Semigroups of linear operators and applications. (1985)
[7] Schechter, M.: Spectra of partial differential operators. (1971) · Zbl 0225.35001
[8] Carlen, E. A.; Carvalho, M. C.; Orlandi, E.: A simple proof stability of fronts for the Cahn--hillaird equation. Commun. math. Phys. 224, 323-340 (2001) · Zbl 1019.35013
[9] Shatah, J.; Strauss, W.: Spectral condition for instability. Contemp. math. 255, 189-198 (2000) · Zbl 0960.47033