Show that the solution u(t, x) of the initial value problem du +ar-; du t > 0, x € R at u(0, x) = f(x) (ƒ € C³(R) given) can be expressed as follows:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Feynman-Kac differential equation question

u(t, x) = E[f(x •exp{3B, + (a – B²)t}]
y?
|dy; t>0.
2t
1
Pri | f(x· exp{ßy + (a – }3²)t} exp
R
Transcribed Image Text:u(t, x) = E[f(x •exp{3B, + (a – B²)t}] y? |dy; t>0. 2t 1 Pri | f(x· exp{ßy + (a – }3²)t} exp R
8.2. Show that the solution u(t, x) of the initial value problem
du
du
+ ar-;
t> 0, x € R
at
u(0, x) = f(x)
(ƒ € C3 (R) given)
can be expressed as follows:
Transcribed Image Text:8.2. Show that the solution u(t, x) of the initial value problem du du + ar-; t> 0, x € R at u(0, x) = f(x) (ƒ € C3 (R) given) can be expressed as follows:
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