Advances in Differential Equations

An identification problem with evolution on the boundary of hyperbolic type

Alfredo Lorenzi and Francesca Messina

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 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

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854678

Mathematical Reviews number (MathSciNet)
MR2643232

Zentralblatt MATH identifier
1196.45016

Subjects
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

Citation

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.


Export citation