Abstract wave equations with acoustic boundary conditions

We define an abstract setting to treat wave equations equipped with time-dependent acoustic boundary conditions on bounded domains of Rn. We prove a well-posedness result and develop a spectral theory which also allows to prove a conjecture proposed in [13]. Concrete problems are also discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

[1]  V. Krasil’nikov.  On the solution of some boundary-contact problems of linear hydrodynamics , 1961 .

[2]  R. Nagel,et al.  Semigroups for Initial-Boundary Value Problems , 2003 .

[3]  Philip Hartman,et al.  Self-adjoint, non-oscillatory systems of ordinary, second order, linear differential equations , 1957 .

[4]  Rainer Nagel,et al.  A Semigroup Approach to Boundary Feedback Systems , 2003 .

[5]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[6]  Wave Propagation in the Ice-Covered Ocean Wave Guide and Operator Polynomials , 2000 .

[7]  Georg Propst,et al.  On Wave Equations with Boundary Dissipation of Memory Type , 1996 .

[8]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[9]  W. Arendt.  Vector-valued laplace transforms and cauchy problems , 2002 .

[10]  Jerome A. Goldstein,et al.  Oscillatory boundary conditions for acoustic wave equations , 2003 .

[11]  Klaus-Jochen Engel,et al.  Decoupling techniques for wave equations with dynamic boundary conditions , 2005 .

[12]  J. Thomas Beale,et al.  Acoustic boundary conditions , 1974 .

[13]  A. Lunardi.  Analytic Semigroups and Optimal Regularity in Parabolic Problems , 2003 .

[14]  S. Krein,et al.  Linear Differential Equations in Banach Space , 1972 .

[15]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[16]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[17]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[18]  H. Fattorini.  Second Order Linear Differential Equations in Banach Spaces , 1985 .