The local backward heat problem

Thi Minh Nhat Vo (1, 2, 3)

1 UO - Université d'Orléans
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 FDP - Fédération de recherche Denis Poisson

In this paper, we study the local backward problem of a linear heat equation with time-dependent coefficients under the Dirichlet boundary condition. Precisely , we recover the initial data from the observation on a subdomain at some later time. Thanks to the " optimal filtering " method of Seidman, we can solve the global backward problem, which determines the solution at initial time from the known data on the whole domain. Then, by using a result of controllability at one point of time, we can connect local and global backward problem.

Mots clés: inverse problem; global backward; local backward; controllability; observation estimate; heat equation

Domaines: Equations aux dérivées partielles [math.AP]

Thi Minh Nhat Vo. The local backward heat problem. 2017. ⟨hal-01508987⟩