Global Existence to a Class of Triangular Block Matrix Cross Diffusion Systems and the Spectral Gap Condition

2023/11/20 by Dung Le, Le, Dung
Computer Science · Mathematics · #35B65 #35J70 #42B37 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.12087

openalex publication_date 2023/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the global existence of classical solutions to cross diffusion systems of m equations on N-dimensional domains (m,N≥2). The diffusion matrix is a triangular block matrix with coupled entries. We establish that the W^1,p norm of solutions for some p>N does not blow up in finite time so that the results in \citeAm2 is applicable. We will also show that the spectral gap condition in \citedlebook,dlebook1 can be relaxed via a new result on BMO norms in \citedleBMO.

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