Abstract
We consider an equation of the type $A(u+k*u)=f$, where $A$ is a linear second-order elliptic operator, $k$ is a scalar function depending on time only and $k*u$ denotes the standard time convolution of functions defined on ${{\bf R}}$ 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.
Citation
Alfredo Lorenzi. Francesca Messina. "An identification problem with evolution on the boundary of parabolic type." Adv. Differential Equations 13 (11-12) 1075 - 1108, 2008. https://doi.org/10.57262/ade/1355867287
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