Logarithmic stability estimates for an inverse source problem from interior measurements

Abstract

This paper deals with an inverse monopolar source problem for the Poisson equation, from interior measurements, whose motivation lies in the sea water intrusion phenomenon. Global logarithmic stability estimates of locations and intensities for monopolar sources in this equation are established. To do that, we make an appropriate choice of a test function allowing to show a stability estimate with respect to boundary conditions and then we use an observability inequality for Laplace equation to control it by the interior measurements. This reveals, on the one hand, the distance between the source and on the other hand the gap between the associated measures.

Keywords:

• Poisson equation
• logarithmic stability estimates
• observability inequality inverse source problems
• electroencephalography/magnetoencephalography
• seawater intrusion

AMS Subject Classifications:

• 35R30
• 35B25
• 35B35
• 35J05
• 35J08
• 65M32

Notes

No potential conflict of interest was reported by the authors.