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

TL;DR

This paper addresses the inverse problem of identifying a space-time dependent source in the Ginzburg-Landau equation using final data, providing theoretical analysis and numerical validation.

Contribution

It introduces a weak-solution framework, derives an explicit gradient formula, and proves existence and uniqueness of quasi-solutions for the inverse problem.

Findings

Explicit gradient formula derived via adjoint system

Existence and uniqueness of quasi-solutions established

Numerical experiments validate the theoretical results

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.