# 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:
 35Q53 KdV-like (Korteweg-de Vries) equations 35R25 Improperly posed problems for PDE
Full Text:
##### 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