Existence and uniqueness of mild and classical solutions of impulsive evolution equations
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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.
CitationAnguraj, A., & Arjunan, M. M. (2005). Existence and uniqueness of mild and classical solutions of impulsive evolution equations. Electronic Journal of Differential Equations, 2005(111), pp. 1-8.
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