Existence and Uniqueness of Local and Global Solutions for a Partial Differential-Algebraic Equation of Index One

2024/11/23 by Benabdallah, Seyyid Ali, Souilah, Messoud
#47B01 #47F05 #47H20 #47N60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.15658

Abstract

In this paper, we use the theory of nonlinear semigroups to establish the existence and uniqueness of both local and global solutions for a partial differential-algebraic equation (PDAE) of index one. This method is applied to a reaction-diffusion system coupled with an elliptic equation in one dimension by transforming the PDAE into a system of linear evolution equations with a Lipschitz-continuous perturbation

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