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Evolutionary Problems Involving Sturm–Liouville Operators

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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

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Abstract

The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in [3], [4] for a special case and extended to more general evolutionary problems, see [7], compare the survey article [5]. The ideas there are utilized for (1 + 1)-dimensional evolutionary problems, which in a particular case results in a hyperbolic partial differential equation with a Sturm–Liouville type spatial operator constrained by an impedance type boundary condition.

Mathematics Subject Classification (2010). Primary 34B24, 35F10, Secondary 35A22, 47G20, 34L40, 35K90, 35L90.

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References

  1. C. Cattaneo. Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantané. C.R. Acad. Sci. Paris I, 247:431, 1958.

    Google Scholar 

  2. R. Leis. Initial boundary value problems in mathematical physics. John Wiley & Sons Ltd. and B.G. Teubner; Stuttgart, 1986.

    Google Scholar 

  3. R. Picard. A Structural Observation for Linear Material Laws in Classical Mathematical Physics. Math. Methods Appl. Sci., 32(14):1768–1803, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Picard. On a Class of Linear Material Laws in Classical Mathematical Physics. Int. J. Pure Appl. Math., 50(2):283–288, 2009.

    MathSciNet  MATH  Google Scholar 

  5. R. Picard. An Elementary Hilbert Space Approach to Evolutionary Partial Differential Equations. Rend. Istit. Mat. Univ. Trieste, 42 suppl.:185–204, 2010.

    Google Scholar 

  6. 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 pp., 2011.

    Google Scholar 

  7. R. Picard. A class of evolutionary problems with an application to acoustic waves with impedance type boundary conditions. Proc. Appl. Math. Mech., 11(1):687–688, 2011.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Analysis, Fachrichtung Mathematik, Technische Universität Dresden, Dresden, Germany

    Rainer Picard

  2. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    Bruce A. Watson

Authors
  1. Rainer Picard
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  2. Bruce A. Watson
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Corresponding author

Correspondence to Rainer Picard .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Picard, R., Watson, B.A. (2014). Evolutionary Problems Involving Sturm–Liouville Operators. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_25

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