A nonlinearly ill-posed problem of reconstructing the temperature from interior data

Alain Pham Ngoc Dinh (1) , Pham Hoang Quan (2) , Dang Duc Trong (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Department of Mathematics and Informatics

We consider the problem of reconstructing, from the interior data $u(x,1)$, a function $u$ satisfying a nonlinear elliptic equation $$ \Delta u = f(x,y,u(x,y)), x \in \RR, y > 0. $$

Mots clés: Fourier transform; Contraction; ill-posedness

Domaines: Equations aux dérivées partielles [math.AP]

Alain Pham Ngoc Dinh, Pham Hoang Quan, Dang Duc Trong. A nonlinearly ill-posed problem of reconstructing the temperature from interior data. Numerical Functional Analysis and Optimization, 2008, 29 (3-4), pp.445-469. ⟨hal-00092402v2⟩