Advances in Differential Equations
- Adv. Differential Equations
- Volume 15, Number 5/6 (2010), 473-502.
An identification problem with evolution on the boundary of hyperbolic type
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.
Adv. Differential Equations Volume 15, Number 5/6 (2010), 473-502.
First available in Project Euclid: 18 December 2012
Permanent link to this document
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. https://projecteuclid.org/euclid.ade/1355854678