Parabolic Differential Equations in Ordered Banach Spaces of Bounded Functions |
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Authors: | Grenon Nathalie Moutoussamy Isabelle Simon Alice Volkmann Peter |
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Institution: | (1) Département de Mathématiques, Université d'Orléans, 45067 Orléans Cedex 2, France;(2) Mathematisches Institut I, Universität Karlsruhe, 76128 Karlsruhe, Germany |
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Abstract: | Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: a,b] × 0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R). |
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Keywords: | existence for parabolic equations parabolic equations in Banach spaces quasimonotonicity |
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