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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.

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