Mild Well-posedness of Abstract Differential Equations

Valentin Keyantuo () and Carlos Lizama ()
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Valentin Keyantuo: University of Puerto Rico, Department of Mathematics Faculty of Natural Sciences
Carlos Lizama: Universidad de Santiago de Chile, Departamento de Matemática Facultad de Ciencias

A chapter in Functional Analysis and Evolution Equations, 2007, pp 371-387 from Springer

Abstract: Abstract We obtain spectral conditions that characterize mild well-posed inhomogeneous differential equations in a general Banach space X. L p periodic solutions of first and second-order equations are considered. The results are expressed in terms of operator-valued Fourier multipliers. Our approach provides a unified framework for various notions of strong and mild solutions. Applications to semilinear equations of second order in Hilbert spaces are given.

Keywords: Hilbert Space; Banach Space; Strong Solution; Mild Solution; Solution Operator (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_24

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DOI: 10.1007/978-3-7643-7794-6_24

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