Positive solutions of some parabolic system with cross-diffusion and\n nonlocal initial conditions

2010/11/15 by Christoph Walker, Walker, Christoph
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1011.3334

openalex publication_date 2010/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is concerned with a system consisting of two coupled nonlinear\nparabolic equations with a cross-diffusion term, where the solutions at\npositive times define the initial states. The equations arise as steady state\nequations of an age-structured predator-prey system with spatial dispersion.\nBased on unilateral global bifurcation methods for Fredholm operators and on\nmaximal regularity for parabolic equations, global bifurcation of positive\nsolutions is derived.\n

Citations

• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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