Abstract
This chapter shows how to apply the integral transform to the single partial differential equation such as Laplace and Wave equations. The basic technique of the integral transform method is demonstrated. Especially, in the case of the time-harmonic response for the 1 and 2D wave equations, the integration path for the inversion integral is discussed in detail with use of the results in Sect. 1.3. At the end of the chapter, the obtained Green's functions are listed in a table so that the reader can easily find the difference of the functional form among the Green's functions. An evaluation technique for a singular inversion integral which arises in a 2D static problem of Laplace equation is also developed.
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Erdélyi A (ed) (1954) Tables of integral transforms, vols I, II, McGraw-Hill, New York
Gradshteyn IS, Ryzhik IM (1980) In: Jefferey A (ed) Table of integrals, series, and products, 5th edn. Academic Press, San Diego
Watson GN (1966) A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge
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Watanabe, K. (2015). Green’s Functions for Laplace and Wave Equations. In: Integral Transform Techniques for Green's Function. Lecture Notes in Applied and Computational Mechanics, vol 76. Springer, Cham. https://doi.org/10.1007/978-3-319-17455-6_2
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DOI: https://doi.org/10.1007/978-3-319-17455-6_2
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