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 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.
An identification problem with evolution on the boundary of parabolic type / A. Lorenzi, F. Messina. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 13:11-12(2008), pp. 1075-1108.
An identification problem with evolution on the boundary of parabolic type
A. LorenziPrimo
;F. MessinaUltimo
2008
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 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.Pubblicazioni consigliate
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