Open AccessConvergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion
Author(s) -
DeHan Chen,
Daijun Jiang
Publication year - 2021
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021023
Subject(s) - tikhonov regularization , regularization (linguistics) , inverse problem , mathematics , minification , inverse , rate of convergence , convergence (economics) , nonlinear system , well posed problem , mathematical optimization , computer science , mathematical analysis , physics , economics , artificial intelligence , channel (broadcasting) , computer network , geometry , quantum mechanics , economic growth
In this paper, we shall study the convergence rates of Tikhonov regularizations for the recovery of the growth rates in a Lotka-Volterra competition model with diffusion. The ill-posed inverse problem is transformed into a nonlinear minimization system by an appropriately selected version of Tikhonov regularization. The existence of the minimizers to the minimization system is demonstrated. We shall propose a new variational source condition, which will be rigorously verified under a Hölder type stability estimate. We will also derive the reasonable convergence rates under the new variational source condition.