Advances in Differential Equations

An identification problem with evolution on the boundary of hyperbolic type

Alfredo Lorenzi and Francesca Messina

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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 second-order dynamical boundary conditions. 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.

Article information

Adv. Differential Equations, Volume 15, Number 5/6 (2010), 473-502.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45Q05: Inverse problems 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 35L20: Initial-boundary value problems for second-order hyperbolic equations


Lorenzi, Alfredo; Messina, Francesca. An identification problem with evolution on the boundary of hyperbolic type. Adv. Differential Equations 15 (2010), no. 5/6, 473--502.

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