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Title: Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts
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.  more » « less
Award ID(s):
2106157
PAR ID:
10553581
Author(s) / Creator(s):
;
Publisher / Repository:
Wiley
Date Published:
Journal Name:
Mathematische Nachrichten
Volume:
297
Issue:
7
ISSN:
0025-584X
Page Range / eLocation ID:
2750 to 2785
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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