Abstract
Mathematical modeling of physical processes yields a system of partial differential equations that describes the behavior of a system physically correct and allows for analytical and numerical predictions of the system behavior. Here we start by shortly summarizing modeling principles which are illustrated for simple linear models in one space dimension. Then this is specified for different types of wave equations.
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References
Carcione, J.M.: Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media. Elsevier (2014). https://doi.org/10.1016/C2013-0-18893-9
Ciarlet, P.G.: Mathematical Elasticity. Vol. I: Three-dimensional Elasticity. Studies in Mathematics and its Applications, vol. 20. North-Holland Publishing Co., Amsterdam (1988). https://doi.org/10.1002/crat.2170250509
Davis, J.L.: Wave propagation in solids and fluids. Springer Science & Business Media (2012). https://doi.org/10.1007/978-1-4612-3886-7
Dörfler, W., Lechleiter, A., Plum, M., Schneider, G., Wieners, C.: Photonic Crystals: Mathematical Analysis and Numerical Approximation, vol. 42. Springer Science & Business Media (2011). https://doi.org/10.1007/978-3-0348-0113-3
Fichtner, A.: Full Seismic Waveform Modelling and Inversion. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer-Verlag, Berlin Heidelberg (2011). https://doi.org/10.1007/978-3-642-15807-0
Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999). https://doi.org/10.1002/3527600434.eap109
Leis, R.: Initial Boundary Value Problems in Mathematical Physics. Courier Corporation (2013). https://doi.org/10.1007/978-3-663-10649-4
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Dörfler, W., Hochbruck, M., Köhler, J., Rieder, A., Schnaubelt, R., Wieners, C. (2023). Modeling of Acoustic, Elastic, and Electro-Magnetic Waves. In: Wave Phenomena. Oberwolfach Seminars, vol 49. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-05793-9_1
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DOI: https://doi.org/10.1007/978-3-031-05793-9_1
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