### 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 language | English |
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Title of host publication | Large-Scale Scientific Computing - 6th International Conference, LSSC 2007, Revised Papers |

Pages | 217-224 |

Number of pages | 8 |

DOIs | |

Publication status | Published - dec. 1 2008 |

Event | 6th International Conference on Large-Scale Scientific Computing, LSSC 2007 - Sozopol, Bulgaria Duration: jún. 5 2007 → jún. 9 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4818 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th International Conference on Large-Scale Scientific Computing, LSSC 2007 |
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Country | Bulgaria |

City | Sozopol |

Period | 6/5/07 → 6/9/07 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*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