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

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-07-24 DOI:10.1016/j.nonrwa.2024.104152

引用次数: 0

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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博弈论中出现的非线性扩散方程的自相似解、正则性和时间渐近性

在这篇文章中，我们研究了一个非线性和非局部的扩散型方程的长期渐近特性，该方程描述了一个相互关联的群体中的石头剪刀布游戏。我们充分描述了自相似解的特征，然后证明初界值问题的解以代数速率收敛于自相似曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.