Advances in Differential Equations

An identification problem with evolution on the boundary of parabolic type

Alfredo Lorenzi and Francesca Messina

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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 ${{\bf R}}$ 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.

Article information

Source
Adv. Differential Equations, Volume 13, Number 11-12 (2008), 1075-1108.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867287

Mathematical Reviews number (MathSciNet)
MR2483131

Zentralblatt MATH identifier
1187.45013

Subjects
Primary: 35R30: Inverse problems
Secondary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 45Q05: Inverse problems

Citation

Lorenzi, Alfredo; Messina, Francesca. An identification problem with evolution on the boundary of parabolic type. Adv. Differential Equations 13 (2008), no. 11-12, 1075--1108. https://projecteuclid.org/euclid.ade/1355867287


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