An inverse problem for the heat equation

Details An inverse problem for the heat equation An inverse problem for the heat equation

2001-02-22

arxiv.org/abs/math-ph/0102029v1

Physics

Mathematical Physics

Scientific paper

Let $u_t = u_{xx} - q(x) u, 0 \leq x \leq 1$, $t>0$, $u(0, t) = 0, u(1, t) = a(t), u(x,0) = 0$, where $a(t)$ is a given function vanishing for $t>T$, $a(t) \not\equiv 0$, $\int^T_0 a(t) dt < \infty$. Suppose one measures the flux $u_x (0,t) := b_0 (t)$ for all $t>0$. Does this information determine $q(x)$ uniquely? Do the measurements of the flux $u_x (1,t) := b(t)$ give more information about $q(x)$ than $b_0 (t)$ does? The above questions are answered in this paper.

Affiliated with

Also associated with

No associations

Rating

An inverse problem for the heat equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An inverse problem for the heat equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An inverse problem for the heat equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-465924