Nonautonomous heat equations with generalized Wentzell boundary conditions

Jin Liang (), Rainer Nagel () and Ti-Jun Xiao ()
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Jin Liang: University of Science and Technology of China, Department of Mathematics
Rainer Nagel: Universität Tübingen, Mathematisches Institut
Ti-Jun Xiao: University of Science and Technology of China, Department of Mathematics

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 321-331 from Springer

Abstract: Abstract In this paper, we study the nonautonomous heat equation in C[0, 1] with generalized Wentzell boundary conditions. It is shown, under appropriate assumptions, that there exists a unique evolution family for this problem and that the family satisfies various regularity properties. This enables us to obtain, for the corresponding inhomogeneous problem, classical and strict solutions having optimal regularity.

Keywords: 35K05; 47D03; 34G10; Nonautonomous heat equations; generalized Wentzell boundary conditions; inhomogeneous Cauchy problems; classical and strict solutions (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_17

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DOI: 10.1007/978-3-0348-7924-8_17

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