Large matrices arising in traveling wave bifurcations

Research output: Conference contribution

Abstract

Traveling wave solutions of reaction-diffusion (semilinear parabolic) systems are studied. The number and stability of these solutions can change via different bifurcations: saddle-node, Hopf and transverse instability bifurcations. Conditions for these bifurcations can be determined from the linearization of the reaction-diffusion system. If an eigenvalue (or a pair) of the linearized system has zero real part, then a bifurcation occurs. Discretizing the linear system we obtain a matrix eigenvalue problem. It is known that its eigenvalues tend to the eigenvalues of the original system as the discretization step size goes to zero. Thus to obtain bifurcation curves we have to study the spectra of large matrices. The general bifurcation conditions for the matrices will be derived. These results will be applied to a reaction-diffusion system describing flame propagation.

Original languageEnglish
Title of host publicationLarge-Scale Scientific Computing - 6th International Conference, LSSC 2007, Revised Papers
Pages217-224
Number of pages8
DOIs
Publication statusPublished - dec. 1 2008
Event6th International Conference on Large-Scale Scientific Computing, LSSC 2007 - Sozopol, Bulgaria
Duration: jún. 5 2007jún. 9 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4818 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Large-Scale Scientific Computing, LSSC 2007
CountryBulgaria
CitySozopol
Period6/5/076/9/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Simon, P. L. (2008). Large matrices arising in traveling wave bifurcations. In Large-Scale Scientific Computing - 6th International Conference, LSSC 2007, Revised Papers (pp. 217-224). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4818 LNCS). https://doi.org/10.1007/978-3-540-78827-0_23