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2008 An identification problem with evolution on the boundary of parabolic type
Alfredo Lorenzi, Francesca Messina
Adv. Differential Equations 13(11-12): 1075-1108 (2008).

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.

Citation

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Alfredo Lorenzi. Francesca Messina. "An identification problem with evolution on the boundary of parabolic type." Adv. Differential Equations 13 (11-12) 1075 - 1108, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1187.45013
MathSciNet: MR2483131

Subjects:
Primary: 35R30
Secondary: 45K05, 45Q05

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 11-12 • 2008
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