Second order abstract initial-boundary value problems [Elektronische Ressource] / vorgelegt von Delio Mugnolo

Second order abstract initial-boundaryvalue problemsDissertationder Fakult at fur Mathematik und Physikder Eberhard-Karls-Universit at Tubingenzur Erlangung des Grades einesDoktors der NaturwissenschaftenVorgelegt vonDelio Mugnoloaus Bari2004IntroductionnPartial di eren tial equations on bounded domains of have traditionally beenequipped with homogeneous boundary conditions (usually Dirichlet, Neumann,or Robin). However, other kinds of boundary conditions can also be considered,and for a number of concrete application it seems that dynamic (i.e., time-dependent) boundary conditions are the right ones.Motivated by physical problems, numerous partial di eren tial equationswith dynamic boundary conditions have been studied in the last decades: H.Amann and J.L. Lions, among others, have investigated elliptic equations (see,e.g., [Li61, Chapt. VI.6], [Hi89], [Gu94], [AF97], and references therein); J. Es-cher has investigated parabolic problems (see [Es93] and andJ.T. Beale and V.N. Krasil’nikov, among others, have investigated second orderhyperbolic equations with dynamical boundary conditions (see [Be76], [Kr61],[Be00], and references therein).In recent years, a systematic study of problems of this kind has been per-formed mainly by A. Favini, J.A. Goldstein, G.R. Goldstein, and S.