Abstract
Let A be an m-accretive operator in a real Banach space X and f : J x X → X a function of Carathéodory type, where J = [0,a] ⊂ ℝ. This paper investigates the existence of mild solutions of the evolution system
satisfying additional time-dependent constraints u(t)∈K(t) on J for a given tube K(·). Main emphasis is on existence results that are valid under minimal assumptions on f, K and X.
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Dedicated to the Remembrance of Philippe Bénilan
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Bothe, D. (2003). Nonlinear evolutions with Carathéodory forcing. In: Arendt, W., Brézis, H., Pierre, M. (eds) Nonlinear Evolution Equations and Related Topics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7924-8_20
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DOI: https://doi.org/10.1007/978-3-0348-7924-8_20
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