Skip to Main Content
Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1186 CAUCHY PROBLEM. FUNDAMENTAL SOLUTIONS
Classical and generalized C auchy problems for ordinary differential equations.
Consider the Cauchy problem for the constant coefficient linear equation (16.2.1.1) (with
a
k
= const) with the initial conditions
w
(k)
t
= b
k
at t = 0; k = 0, 1, . . . , m 1, (16.2.1.5)
where the b
k
are some constants.
Let w(t) be the classical solution of the Cauchy problem for t > 0. We extend the
functions w(t) and f(t) by zero into the domain t < 0. Let us denote the extended functions
by w
+
and f
+
. We have
w
+
= ϑ(t)w(t), f
+
= ϑ(t)f (t). (16.2.1.6)
By successively differentiating the first relation in (16.2.1.6) and by taking into
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Differential Equations, 2nd Edition

Differential Equations, 2nd Edition

Steven G. Krantz

Publisher Resources

ISBN: 9781466581494