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Linear Partial Differential Equations with Constant Coefficients: an Elementary Proof of an Existence Theorem
Published online by Cambridge University Press: 21 January 2009
Extract
We consider a linear partial differential equation with constant coefficients in one dependent and m independent variables, the right-hand side being zero,
P being a symbolic polynomial in D1, …, Dm. If P can be decomposed into two factors, so that the equation can be written
it is evident that the sum of any solution of
and any solution of
is also a solution of (1).
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- Copyright © Edinburgh Mathematical Society 1959