Spectrum of some integro-differential operators and stability of travelling waves

Arnaud Ducrot (1) , Martine Marion (2, 3) , Vitaly Volpert (4, 5)

1 IMB - Institut de Mathématiques de Bordeaux
2 MMCS - Modélisation mathématique, calcul scientifique
3 ECL - École Centrale de Lyon
4 ICJ - Institut Camille Jordan
5 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis

Spectral properties of some integro-differential operators on R1 are studied. Characterization of the principal eigenvalue is obtained in terms of the positive eigenfunction. These results are used to prove local and global stability of travelling waves and to find their speed.

Domaines: Equations aux dérivées partielles [math.AP]

Arnaud Ducrot, Martine Marion, Vitaly Volpert. Spectrum of some integro-differential operators and stability of travelling waves. Nonlinear Analysis: Theory, Methods and Applications, 2011, 74 (13), pp.4455-4473. ⟨10.1016/j.na.2011.04.009⟩. ⟨hal-00653653⟩