Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 6 / 2 / b

Table of contents
- Solution b

Solution

The damped free-transport evolution is

S (t) h (x, v) = e^{- t} h (x - t v, v)

. Substituting it into the Duhamel principle gives

f (t, x, v) = e^{- t} f_{0} (x - t v, v) + \int_{0}^{t} e^{- (t - s)} g (s, x - (t - s) v, v) d s .

The spatial shifts all follow the same backward characteristic curve ending at

(x, v)

t

; the velocity is constant.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version