Existence and uniqueness of mild and classical solutions of impulsive evolution equations

Date
2005-10-17
Authors
Anguraj, Annamalai
Arjunan, Mani Mallika
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We consider the non-linear impulsive evolution equation u'(t) = Au(t) + ƒ(t, u(t), Tu(t), Su(t)), 0 < t < T0, t ≠ ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, 3,..., p. in a Banach space X, where A is the infinitesimal generator of a C0 semigroup. We study the existence and uniqueness of the mild solutions of the evolution equation by using semigroup theory and then show that the mild solutions give rise to a classical solutions.
Description
Keywords
Semigroups, Evolution equations, Impulsive conditions
Citation
Anguraj, A., & Arjunan, M. M. (2005). Existence and uniqueness of mild and classical solutions of impulsive evolution equations. <i>Electronic Journal of Differential Equations, 2005</i>(111), pp. 1-8.