Carleman Linearization of Partial Differential Equations

2024/11/14 by Tamas Vaszary, Vaszary, Tamas · 2 citations
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2412.00014

openalex publication_date 2024/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Carleman linearization is a technique that embeds systems of ordinary differential equations with polynomial nonlinearities into infinite dimensional linear systems in a procedural way. In this paper we generalize the method for systems of partial differential equations with quadratic nonlinearities, while maintaining the original structure of Carleman linearization. Furthermore, we apply our approach to Burger's equation and to the Vlasov equation as examples.

Cited by

• Beyond Carleman Linearization of Nonlinear Dynamical System: Insights from a Case Study
• Globalizing the Carleman linear embedding method for nonlinear dynamics

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