Identification of Source Terms in the Ginzburg-Landau Equation from Final Data

2025/11/10 by Roberto Morales, Morales, Roberto, Javier-Ramírez-Ganga
Engineering · Mathematics · #35Q56 #35R30 #49N45 #65N21 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2511.07345

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's functional, deriving an explicit gradient formula via an adjoint system and proving its Lipschitz continuity. We then establish existence and uniqueness results for quasi-solutions, and validate the theory with numerical experiments based on iterative methods.

Citations

• Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data
• Local null controllability of a cubic Ginzburg-Landau equation with dynamic boundary conditions
• Pattern formation outside of equilibrium

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