Initial Value Inverse Problem of a Convection-Diffusion Equation with Integral Source Term

doi:10.13438/j.cnki.jdzk.2024.05.002

Abstract

Abstract: This paper mainly discusses the initial value inverse problem of a convection-diffusion equation with integral source term.Based on the optimal control framework,the existence of the optimal solution for the control functional is proved,and the necessary condition for the optimal solution is deduced.Finally,with the necessary conditions,non-local uniqueness and stability of the optimal solution are proved by the prior estimates of the forward problem.

Key words: integral source term, inverse problem, optimal control, uniqueness, stability

QIAN Kun, TAN Ruixia, FENG Lixiang. Initial Value Inverse Problem of a Convection-Diffusion Equation with Integral Source Term[J]. Journal of Jishou University(Natural Sciences Edition), 2024, 45(5): 11-16.

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