A Class of Evolutionary Problems with an Application to Acoustic Waves with Impedance Type Boundary Conditions

  • Rainer PicardEmail author
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)


A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition is imposed which in the time-harmonic case corresponds to an impedance or Robin boundary condition. Memory and delay effects in the interior and also on the boundary are built into the problem class.


Evolution equations partial differential equations causality acoustic waves impedance type boundary condition memory delay 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Leis. Initial boundary value problems in mathematical physics. John Wiley & Sons Ltd. and B.G. Teubner; Stuttgart, 1986.zbMATHGoogle Scholar
  2. 2.
    R. Picard. A Structural Observation for Linear Material Laws in Classical Mathematical Physics. Math. Methods Appl. Sci., 32 (14):1768-1803, 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    R. Picard. On a Class of Linear Material Laws in Classical Mathematical Physics. Int. J. Pure Appl. Math., 50 (2):283-288, 2009.MathSciNetzbMATHGoogle Scholar
  4. 4.
    R. Picard. An Elementary Hilbert Space Approach to Evolutionary Partial Differential Equations. Rend. Istit. Mat. Univ. Trieste, 42 suppl.: 185-204, 2010.MathSciNetzbMATHGoogle Scholar
  5. 5.
    R. Picard and D.F. McGhee. Partial Differential Equations: A unified Hilbert Space Approach, volume 55 of De Gruyter Expositions in Mathematics. De Gruyter. Berlin, New York. 518 p., 2011. To appear.CrossRefGoogle Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Institut für Analysis, Fachrichtung MathematikTechnische Universität DresdenDresdenGermany

Personalised recommendations