Second order parabolic equations in Banach spaces with dynamic boundary conditions

Xiao, Ti-Jun; Liang, Jin

doi:10.1090/S0002-9947-04-03704-3

Second order parabolic equations in Banach spaces with dynamic boundary conditions
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by Ti-Jun Xiao and Jin Liang

Trans. Amer. Math. Soc. 356 (2004), 4787-4809

DOI: https://doi.org/10.1090/S0002-9947-04-03704-3

Published electronically: June 25, 2004

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Abstract:

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

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