Data di Pubblicazione:
2010
Citazione:
An identification problem with evolution on the boundary of hyperbolic type / A. Lorenzi, F. Messina. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 15:5-6(2010), pp. 473-502.
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 in $(-\infty,T)$ with their supports in $[0,T]$. The previous equation is endowed with dynamical boundary conditions.
\pn
Assuming that the kernel $k$ is unknown and a supplementary condition is given, $k$ can be recovered and global existence, uniqueness and continuous dependence results can be shown.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Elliptic equations with time convolutions. Dynamical boundary conditions. Determination of an unknown kernel. Semigroup theory. Applications to physical and biological problems.
Elenco autori:
A. Lorenzi, F. Messina
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