Applications to Partial Differential Equations

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

Chapter Chapter 10 in Generalized Functions, 2004, pp 265-311 from Springer

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

Keywords: Partial Differential Equation; Wave Equation; Fundamental Solution; Light Cone; Inverse Fourier Transform (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8174-6_10

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