### Author Topic: inhomogeneous b.c.  (Read 2891 times)

#### Thomas Nutz

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##### inhomogeneous b.c.
« on: October 05, 2012, 08:59:09 AM »
In the 10th lecture we are asked to consider
$$0=\int_{II}G(x,y,t-\tau)(-u_{\tau}(y,\tau))+ku_{yy}(y,\tau)d\tau'dy$$

1. question: What are we integrating over here? Is $\tau'=t-\tau$?

2. Where is this expression coming from? Is it a trial solution that I simply have to take as given, or does it follwow from any other expression?

Thanks!

#### Victor Ivrii

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##### Re: inhomogeneous b.c.
« Reply #1 on: October 05, 2012, 10:42:42 AM »
In the 10th lecture we are asked to consider
$$0=\int_{II}G(x,y,t-\tau)(-u_{\tau}(y,\tau))+ku_{yy}(y,\tau)d\tau'dy$$

1. question: What are we integrating over here? Is $\tau'=t-\tau$?

2. Where is this expression coming from? Is it a trial solution that I simply have to take as given, or does it follwow from any other expression?

Thanks!

$'$ is an artefact (removed). BTW domain is $\Pi$, not $II$

$\bigl(-u_{\tau}(y,\tau)+ku_{yy}(y,\tau)\bigr)=0$ due to equation $u_t-ku_{xx}=0$ (if $u_t-ku_{xx}=f$) we would get an extra term (17) in the lecture 10