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Session S18 - Recent progress in non-linear PDEs and their applications

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A Mathematical Model of Wealth Distribution Through an Amenities-Based Theory

Lyndsey Wong

University of Colorado Boulder, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Gentrification refers to the influx of income into a community leading to the improvement of an area through renovation or the introduction of local amenities. This is usually accompanied by an increase in the cost of living, which displaces lower income populations. To better understand this problem, we will introduce a model for the dynamics of wealth based on amenities. In order to find when we have inhomogeneous solutions to this model, we present two approaches. The first is to perform a linear stability analysis in order to find when small perturbations of constant equilibrium solutions become unstable. The second is to prove the existence of a global bifurcation of these solutions from the constant equilibrium solution.

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