Determination of source terms in a degenerate parabolic equation. (English) Zbl 1200.35319

Cannarsa, P.; Tort, J.; Yamamoto, M.

Inverse Probl. 26, No. 10, Article ID 105003, 20 p. (2010).

Summary: We prove Lipschitz stability results for inverse source problems relative to parabolic equations. We use the method introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates. What is new here is that we study a class of one-dimensional degenerate parabolic equations. In our model, the diffusion coefficient vanishes at one extreme point of the domain. Instead of the classical Carleman estimates obtained by Fursikov and Imanuvilov for non degenerate equations, we use and extend some recent Carleman estimates for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble. Finally, we obtain Lipschitz stability results in inverse source problems for our class of degenerate parabolic equations both in the case of a boundary observation and in the case of a locally distributed observation.

MSC:

35R30	Inverse problems for PDEs
35B35	Stability in context of PDEs
35K65	Degenerate parabolic equations

Keywords:

inverse problems; stability; boundedness; parabolic partial differential equations of degenerate type; inverse problems