# 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)
Computation of spiral spectra. (English) Zbl 1093.35014
Summary: A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius $R$ increases, the eigenvalue spectra converge to the absolute spectrum predicted by Sandstede and Scheel. The convergence rate is consistent with $1/R$, except possibly near the edge of the spectrum. Eigenfunctions computed on large disks are compared with predicted exponential forms. Away from the edge of the absolute spectrum the agreement is excellent, while near the edge computed eigenfunctions deviate from predictions, probably due to finite-size effects. In addition to eigenvalues associated with the absolute spectrum, computations reveal point eigenvalues. The point eigenvalues and associated eigenfunctions responsible for both core and far-field break-up of spiral waves are shown.
##### MSC:
 35B30 Dependence of solutions of PDE on initial and boundary data, parameters 35K57 Reaction-diffusion equations 74J30 Nonlinear waves (solid mechanics) 92C99 Physiological, cellular and medical topics 35P20 Asymptotic distribution of eigenvalues and eigenfunctions for PD operators