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Partial Differential Equations and Mathematical Physics pp 13–29Cite as

Birkhäuser

On Exact Solutions of Linear PDEs

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 52))

Abstract

The role of exact fundamental solutions in the study of linear PDEs is illustrated by several examples among equations of mixed type, subelliptic and degenerate elliptic equations, and hyperbolic equations. In particular, we derive exact fundamental solutions for the degenerate hyperbolic operators \( \partial _t^2 - {\partial ^{2l}}\vartriangle \) in \( {{\mathbb{R}}^{{2p}}} \times \mathbb{R} \) for arbitrary1 p =1, 2,….

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Author information

Authors and Affiliations

  1. Department of Mathematics, Yale University, Box 208283, New Haven, CT, 06520-8283

    Richard Beals

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  1. Richard Beals
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Editors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, Ibaraki, 305, Japan

    Kunihiko Kajitani

  2. MATHS-Université Paris VI, BC 172, 4 Place Jussieu, Paris Cedex 05, 75252, France

    Jean Vaillant

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Beals, R. (2003). On Exact Solutions of Linear PDEs. In: Kajitani, K., Vaillant, J. (eds) Partial Differential Equations and Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 52. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0011-6_2

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  • DOI: https://doi.org/10.1007/978-1-4612-0011-6_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6572-6

  • Online ISBN: 978-1-4612-0011-6

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