Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations
Analysis of PDEs
2026-02-25 v1 Mathematical Physics
math.MP
Abstract
This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global well-posedness of the reference and the approximating systems is established under natural assumptions. In addition, it is shown that the approximating solution converges exponentially to the solution of the reference system, provided the observational resolution and the nudging parameter are suitably chosen. The approach allows us to consider many systems, such as the Allen-Cahn, Cahn-Hilliard, Sellers-type energy balance, and bidomain systems, for the first time.
Keywords
Cite
@article{arxiv.2602.20769,
title = {Continuous Data Assimilation for Semilinear Parabolic Equations: A General Approach by Evolution Equations},
author = {Gianmarco Del Sarto and Matthias Hieber and Filippo Palma and Tarek Zöchling},
journal= {arXiv preprint arXiv:2602.20769},
year = {2026}
}