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Analysis and Computation of Hyperbolic PDEs with Random Data

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Encyclopedia of Applied and Computational Mathematics

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Introduction

Hyperbolic partial differential equations (PDEs) are mathematical models of wave phenomena, with applications in a wide range of scientific and engineering fields such as electromagnetic radiation, geosciences, fluid and solid mechanics, aeroacoustics, and general relativity. The theory of hyperbolic problems, including Friedrichs and Kreiss theories, has been well developed based on energy estimates and the method of Fourier and Laplace transforms [8, 16]. Moreover, stable numerical methods, such as the finite difference method [14], the finite volume method [17], the finite element method [6], the spectral method [4], and the boundary element method [11], have been proposed to compute approximate solutions of hyperbolic problems. However, the development of the theory and numerics for hyperbolic PDEs has been based on the assumption that all input data, such as coefficients, initial data, boundary and force terms, and computational domain, are exactly known.

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Author information

Authors and Affiliations

  1. Division of Mathematics and Computational Sciences and Engineering (MCSE), King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Mohammad Motamed

  2. Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Milan, Italy

    Fabio Nobile

  3. Division of Mathematics and Computational Sciences and Engineering (MCSE), King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Raúl Tempone

Authors
  1. Mohammad Motamed
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  2. Fabio Nobile
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  3. Raúl Tempone
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Editor information

Editors and Affiliations

  1. University of Texas at Austin, Austin, TX, USA

    Björn Engquist

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Motamed, M., Nobile, F., Tempone, R. (2015). Analysis and Computation of Hyperbolic PDEs with Random Data. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_527

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