Self-similar solutions, regularity and time asymptotics for a nonlinear diffusion equation arising in game theory
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909259634049024 |
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| author | Fontelos, Marco Antonio Salvarani, Francesco Duteil, Nastassia Pouradier |
| author_facet | Fontelos, Marco Antonio Salvarani, Francesco Duteil, Nastassia Pouradier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12365 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar solutions, regularity and time asymptotics for a nonlinear diffusion equation arising in game theory Fontelos, Marco Antonio Salvarani, Francesco Duteil, Nastassia Pouradier Analysis of PDEs 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. |
| title | Self-similar solutions, regularity and time asymptotics for a nonlinear diffusion equation arising in game theory |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.12365 |