Open AccessA STRONGLY ILL-POSED INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
Author(s) -
Alfredo Lorenzi
Publication year - 2013
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2013.804891
Subject(s) - mathematics , boundary value problem , mathematical analysis , dirichlet boundary condition , uniqueness , mixed boundary condition , domain (mathematical analysis) , robin boundary condition , boundary (topology) , free boundary problem , cauchy boundary condition
Via Carleman estimates we prove uniqueness and continuous dependence results for an identification and strongly ill-posed linear integro-differential parabolic problem with the Dirichlet boundary condition, but with no initial condition. The additional information consists in a boundary linear integral condition involving the normal derivative of the temperature on the whole of the lateral boundary of the space-time domain.