A PARABOLIC INVERSE PROBLEM WITH AN UNKNOWN BOUNDARY-CONDITION Academic Article

abstract

• In this paper we consider a parabolic inverse problem in which an unknown function is involved in the boundary condition, and we attempt to recover this function by measuring the value of the temperature at a fixed point on the boundary. The motivation for studying this problem arises from some physical models such as a heat conduction system where the heat exchange between the system and its surrounding is unknown. We apply the singularity estimates for the fundamental solution of a parabolic equation along with the generalized Bellman-Gronwall inequality to obtain the continuous dependence of the solution upon the known data. Uniqueness of the solution is established as a direct corollary. 1990.

authors

• Rundell, William

published proceedings

• JOURNAL OF DIFFERENTIAL EQUATIONS

author list (cited authors)

• RUNDELL, W., & YIN, H. M.

citation count

• 6

complete list of authors

• RUNDELL, W||YIN, HM

publication date

• August 1990

publisher

• Elsevier  Publisher

published in

• Journal of Differential Equations  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4905 Statistics

Digital Object Identifier (DOI)

• 10.1016/0022-0396(90)90031-J

start page

• 234

end page

• 242

volume

• 86

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2F0022-0396%2890%2990031-j