On the existence of solutions for a class of systems of integro-differential equations with the logarithmic Laplacian and drift

2024/06/12 by Yuming Chen, Chen, Yuming, Vitali Vougalter +1
Mathematics · #35P05 #45K05 #47G20 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.08325

openalex publication_date 2024/06/12 · openalex created_date 2024/06/14 · openalex updated_date 2026/07/28

Abstract

In this article, we consider a system of integro-differential equations in L²(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear operators associated with the system satisfy the Fredholm property. By virtue of a fixed point technique, we demonstrate the existence of solutions. We emphasize that the discussion is more complicated than that of the scalar situation as there are more cumbersome technicalities to overcome.

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