Bounded Solutions of Parabolic Equations in Continuous Function Spaces

Authors: Gaston N'Guerekata, Nguyễn Văn Minh, James Liu, Vũ Quốc Phóng,

https://doi.org/10.1619/fesi.49.337

Publisher, magazine: ,

Publication year: 2006

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Abstract

This paper is concerned with the existence of bounded mild solutions to equations of the form u′(t) = Au(t) + f(t), where A generates a holomorphic semigroup that is not necessarily strongly continuous, and f is a bounded function. This problem arises when one considers a parabolic equation in spaces of continuous functions. The obtained results, that are stated in terms of spectral properties of the spectrum of A and the uniform spectrum of f, extend previous ones.

Tags: Parabolic equation, Continuous function space, Complete second order evolution equation, Mild solution