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Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts.
- Source :
-
Mathematische Nachrichten . Jul2024, Vol. 297 Issue 7, p2750-2785. 36p. - Publication Year :
- 2024
-
Abstract
- We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 297
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 178333608
- Full Text :
- https://doi.org/10.1002/mana.202300273