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arXiv · 2407.12365

Self-similar solutions, regularity and time asymptotics for a nonlinear diffusion equation arising in game theory

Marco Antonio Fontelos·Francesco Salvarani·Nastassia Pouradier Duteil
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Abstract

In this article, we study the long-time asymptotic properties of a non-linear and non-local equation of diffusive type which describes the rock-paper-scissors game in an interconnected population.We fully characterize the self-similar solution and then prove that the solution of the initial-boundary value problem converges to the self-similar profile with an algebraic rate.

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Marco Antonio Fontelos, Francesco Salvarani, Nastassia Pouradier Duteil. 2024-07-17. Self-similar solutions, regularity and time asymptotics for a nonlinear diffusion equation arising in game theory. https://arxiv.org/abs/2407.12365

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