Second order parabolic equations in Banach spaces with dynamic boundary conditions

Ti-Jun Xiao, Jin Liang
2004 Transactions of the American Mathematical Society  
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.
doi:10.1090/s0002-9947-04-03704-3 fatcat:tauk6j2epzcdnd3kibrllggnwq