### An identification problem with evolution on the boundary of parabolic type

#### 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.

#### Article information

Source
Adv. Differential Equations, Volume 13, Number 11-12 (2008), 1075-1108.

Dates
First available in Project Euclid: 18 December 2012