We prove uniqueness and continuous dependence results for a severely ill-posed linear integrodifferential boundary-value parabolic problem with no initial condition. This latter condition is replaced with an additional boundary information prescribing the temperature on an open subset of the geometric domain . The integral operators entering the equation are defined by integrals of Volterra type with respect to time. In particular, the class of integrodifferential equations dealt with in this paper include those occurring in the linear theory of heat flow in a rigid body consisting of a material with thermal memory.
Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator / A. Lorenzi, F. Messina. - In: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - ISSN 0928-0219. - 21:2(2013 Apr), pp. 281-309.
|Titolo:||Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator|
LORENZI, ALFREDO (Primo)
MESSINA, FRANCESCA (Ultimo)
|Parole Chiave:||Ill-posed problems, linear parabolic integrodifferential equations, no initial conditions, uniqueness, approximation results.|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||apr-2013|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1515/jip-2012-0047|
|Appare nelle tipologie:||01 - Articolo su periodico|