## An inverse problem for the heat equation.(English)Zbl 0987.35164

Summary: 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 $$t>T$$, $$a(t)\not\equiv 0$$, $$\int^T_0a(t)dt <\infty$$. 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? These questions are answered in this note.

### MSC:

 35R30 Inverse problems for PDEs 35K05 Heat equation

### Keywords:

coefficient reconstruction; uniqueness; heat transfer
Full Text:

### References:

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