Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion

DOI10.3934/ipi.2021023zbMath1473.35649OpenAlexW3136347877MaRDI QIDQ1983445

Daijun Jiang, De-Han Chen

Publication date: 10 September 2021

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2021023

zbMATH Keywords

convergence ratesTikhonov regularizationvariational source conditionLotka-Volterra competition model with diffusion

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Inverse problems for PDEs (35R30) Rate of convergence, degree of approximation (41A25) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

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• Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
• An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems
• Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
• Bifurcation structures of positive stationary solutions for a Lotka-Volterra competition model with diffusion. II: Global structure
• Generation of interfaces for Lotka--Volterra competition--diffusion system with large interaction rates
• Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model.
• Dynamics of Lotka-Volterra competition systems with large interaction
• The biology of numbers. The correspondence of Vito Volterra on mathematical biology
• Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions
• Simultaneous reconstruction of the initial temperature and heat radiative coefficient
• Theory and examples of variational regularization with non-metric fitting functionals
• The inverse problem of determining several coefficients in a nonlinear Lotka–Volterra system
• Elastic-net regularization versus ℓ ¹ -regularization for linear inverse problems with quasi-sparse solutions
• Generalized Bregman distances and convergence rates for non-convex regularization methods
• Convergence rates for Tikhonov regularization of coefficient identification problems in Laplace-type equations
• Dynamics of strongly competing systems with many species
• Convergence rates of Tikhonov regularizations for parameter identification in a parabolic-elliptic system
• Parameter choice in Banach space regularization under variational inequalities
• Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Carleman estimates for parabolic equations and applications
• Abstract Parabolic Evolution Equations and their Applications
• Positive solutions for a three-species competition system with diffusion—I. General existence results
• Positive solutions for a three-species competition system with diffusion—II. The case of equal birth rates
• A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction
• Variational source condition for ill-posed backward nonlinear Maxwell’s equations
• Convergence rates inℓ¹-regularization if the sparsity assumption fails
• Parameter identification in a structured population model
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods
• On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization
• Verification of a variational source condition for acoustic inverse medium scattering problems
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity