Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

Mokhtar Kirane (1) , Salman Amin Malik (1)

1 MIA - Mathématiques, Image et Applications - EA 3165

We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

Mots clés: Fourier series; Inverse problem; Fractional derivative; Heat equation; Integral equations; Biorthogonal system of functions; Fourier series.

Domaines: Equations aux dérivées partielles [math.AP]

Mokhtar Kirane, Salman Amin Malik. Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time. 2010. ⟨hal-00549130⟩