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)
Instability of homogeneous periodic solutions of parabolic-delay equations. (English) Zbl 0811.35156

Parabolic systems of the form

u t=DΔu(x,t)+fu t (x,·)(1)

are considered, where f:C([-r,0], N ) N and D is an N×N real matrix with spectrum in the right half plane. The first part is concerned mainly with fairly standard existence and uniqueness results for equation (1) using the abstract form u ˙=Au+f(u t ) and the variation of constants formula.

In the second part, the existence of travelling waves of (1) is proved under the assumption that the reaction equation u ˙(t)=f(u t ) has a non-constant periodic solution. The destabilizing effect of the D matrix is shown by considering a variational form of (1) and the corresponding reaction equation. If a characteristic multiplier has absolute value greater than 1 then the travelling wave is unstable.

35R10Partial functional-differential equations
35K57Reaction-diffusion equations