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Nonlinear PDE. Singularities, Propagation, Applications

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Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations

Part of the book series: Operator Theory: Advances and Applications ((APDE,volume 145))

Abstract

This text deals with the singularities of the solutions of several classes of nonlinear partial differential equations and systems. Applications of the results here obtained are given for the Monge—Ampère equation, for quasi-linear systems arising in fluid mechanics, and for some nonlinear integrodifferential equations useful in solid body mechanics in media with memory. In our investigations we have used two different approaches — the classical method of characteristics in the case of systems with one space variable and the machinery of paradifferential operators in the multi­dimensional case.

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  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, 1113, Bulgaria

    P. R. Popivanov

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  1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, 53115, Germany

    Sergio Albeverio

  2. Institut für Mathematik, Technische Universität Clausthal, Clausthal-Zellerfeld, 38678, Germany

    Michael Demuth

  3. Institut für Mathematik, Universität Potsdam, Potsdam, 14415, Germany

    Elmar Schrohe  & Bert-Wolfgang Schulze  & 

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Popivanov, P.R. (2003). Nonlinear PDE. Singularities, Propagation, Applications. In: Albeverio, S., Demuth, M., Schrohe, E., Schulze, BW. (eds) Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations. Operator Theory: Advances and Applications, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8073-2_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8073-2_1

  • Publisher Name: Birkhäuser, Basel

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