## Inverse problems for parabolic equations.(English)Zbl 1162.35384

Summary: Let $$u_t-\nabla^2u=f(x)\: =\sum^M_{m=1}a_m\delta(x-x_m)$$ in $$D\times[0,\infty)$$, where $$D\subset {\mathbb R}^3$$ is a bounded domain with a smooth connected boundary $$S$$, $$a_m=\text{ const}, \delta(x-x_m)$$ is the delta-function. Assume that $$u(x,0)=0, u=0$$ on $$S$$. Given the extra data $$u(y_k,t)\: = b_k(t)$$, $$1\leq k\leq K$$, can one find $$M, a_m$$, and $$x_m$$? Here $$K$$ is some number. An answer to this question and a method for finding $$M, a_m$$, and $$x_m$$ are given.

### MSC:

 35K20 Initial-boundary value problems for second-order parabolic equations 35R30 Inverse problems for PDEs