
1114 SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
The vector equation (17) consists of three independent scalar equations; i.e., we have
obtained complete decomposition of the original system (12) in this case. In the special
case of Λ = Ω = ∇, formulas (16) and Eq. (17) become (8) and (11), respectively.
The general solution of the homogeneous equation (17) with f= 0 and KΩ·Λ 6= const L
can be represented in the form of the sum
w = w
1
+ w
2
,
where w
1
and w
2
are arbitrary solutions of the two simpler equations
L[w
1
] = 0,
L + KΩ · Λ
[w
2
] = 0.
⊙ Literature for Section 12.19: A. D. Polyanin and A. I. Zhurov (2013), A. D. Polyanin and S. A. Lychev
(2014a,b), ...