Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion. (English) Zbl 1473.35649
Summary: 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.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 41A25 | Rate of convergence, degree of approximation |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 92D25 | Population dynamics (general) |
Keywords:
Lotka-Volterra competition model with diffusion; Tikhonov regularization; convergence rates; variational source conditionReferences:
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