Applications to Partial Differential Equations

Ram P. Kanwal
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Ram P. Kanwal: The Pennsylvania State University, Department of Mathematics

Chapter 10 in Generalized Functions Theory and Technique, 1998, pp 256-296 from Springer

Abstract: Abstract Recall from Chapter 2 that the differential operator L of order p in n independent variables x1, x2,...,x n ,is 1 $$Lu=\sum\limits_{\left| k \right|\le p}{{{a}_{k}}}\left( x \right){{D}^{k}}u$$ where the coefficients a k have partial derivatives of all orders. Its formal adjoint L* is defined as 2 $${{L}^{*}}v={{\sum\limits_{\left| k \right|\le p}{\left( -1 \right)}}^{k}}{{D}^{k}}\left( {{a}_{k}}v \right)$$ Here u and v are functions having derivatives of order p in R n .

Keywords: Partial Differential Equation; Fundamental Solution; Light Cone; Inverse Fourier Transform; Wave Operator (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4684-0035-9_10

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