Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates

Abstract

We consider a fractional radiative transport equation, where the time derivative is of half order in the Caputo sense. By establishing Carleman estimates, we prove the global Lipschitz stability in determining the coefficients of the one-dimensional time-fractional radiative transport equation of half-order.

Keywords:

• Fractional radiative transport equation
• Carleman estimate
• global Lipschitz stability

AMS Classifications:

• 35R09
• 35R11
• 35R30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the interdisciplinary project on environmental transfer of radionuclides from University of Tsukuba and Hirosaki University and by the A3 foresight program ‘Modeling and Computation of Applied Inverse Problems’ of the Japan Society of the Promotion of Science. MM also acknowledges support from Grant-in-Aid for Scientific Research (17K05572 and 17H02081) of the Japan Society for the Promotion of Science (JSPS).