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An identification problem with evolution on the boundary of parabolic type. (English) Zbl 1187.45013
Summary: We consider an equation of the type $$A(u+k\ast u)=f$$, where $$A$$ is a linear second-order elliptic operator, $$k$$ is a scalar function depending on time only and $$k\ast u$$ denotes the standard time convolution of functions defined on $$\mathbb{R}$$ with their supports in $$[0,T]$$. The previous equation is endowed with dynamical boundary conditions.
Assuming that the kernel $$k$$ is unknown and information is given, under suitable additional conditions $$k$$ can be recovered and global existence, uniqueness and continuous dependence results can be shown.

##### MSC:
 45Q05 Inverse problems for integral equations 45K05 Integro-partial differential equations 35K99 Parabolic equations and parabolic systems