Existence and Uniqueness of Local Solutions for a Class of Partial Differential-Algebraic Equations

2025/02/10 by Seyyid Ali Benabdallah, Benabdallah, Seyyid Ali
Mathematics · #47B01 #47F05 #47H20 #47N60 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2502.06454

openalex publication_date 2025/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the existence of a unique local solution. The analysis relies on techniques from functional analysis, semi-group theory, and the theory of differential-algebraic systems. Additionally, we provide applications to illustrate the effectiveness of this result.

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