Similarity solutions for a multi-dimensional replicator dynamics equation

被引：7
|
作者：
Papanicolaou, Vassilis G. [1 ]
Smyrlis, George [2 ]
机构：
[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece
[2] Inst Educ Technol, Dept Math, Athens 12210, Greece
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 7-8期
关键词：
Replicator dynamics problem; Self-similar solutions; Nonlinear degenerate parabolic PDE with a nonlocal term; Laplacian;
D O I：
10.1016/j.na.2009.01.227
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a one-parameter family of self-similar solutions for a nonlinear degenerate multi-dimensional parabolic equation containing a nonlocal term. All these solutions are strictly positive and their integral over the whole space is 1. The equation serves as a replicator dynamics model where the set of strategies is a continuum. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3185 / 3196
页数：12
相关论文
共 50 条
  • [1] Similarity solutions for a replicator dynamics equation
    Kravvaritis, Dimitrios C.
    Papanicolaou, Vassilis G.
    Yannacopoulos, Athanassios N.
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (04) : 1929 - 1945
  • [2] SIMILARITY SOLUTIONS OF A MULTIDIMENSIONAL REPLICATOR DYNAMICS INTEGRODIFFERENTIAL EQUATION
    Papanicolaou, Vassilis G.
    Vasilakopoulou, Kyriaki
    JOURNAL OF DYNAMICS AND GAMES, 2016, 3 (01): : 51 - 74
  • [3] SIMILARITY SOLUTIONS OF A REPLICATOR DYNAMICS EQUATION ASSOCIATED WITH A CONTINUUM OF PURE STRATEGIES
    Papanicolaou, Vassilis G.
    Vasilakopoulou, Kryriaki
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
  • [4] Stability of the replicator equation for a single species with a multi-dimensional continuous trait space
    Cressman, R
    Hofbauer, J
    Riedel, F
    JOURNAL OF THEORETICAL BIOLOGY, 2006, 239 (02) : 273 - 288
  • [5] Source-Solutions for the Multi-dimensional Burgers Equation
    Serre, Denis
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2021, 239 (01) : 95 - 116
  • [6] Source-Solutions for the Multi-dimensional Burgers Equation
    Denis Serre
    Archive for Rational Mechanics and Analysis, 2021, 239 : 95 - 116
  • [7] PERIODIC SOLUTIONS OF A MULTI-DIMENSIONAL CAHN-HILLIARD EQUATION
    Liu, Ji
    Wang, Yifu
    Zheng, Jiashan
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
  • [8] A multi-dimensional functional equation having cubic forms as solutions
    Park, Won-Gil
    Bae, Jae-Hyeong
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (08): : 5238 - 5244
  • [9] On the Solutions of Multi-dimensional Clairaut Equation with Multi-homogeneous Function of the Derivatives
    Rakhmelevich, I., V
    IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2014, 14 (04): : 374 - 381
  • [10] Multi-dimensional symbolic dynamics
    Lind, D
    SYMBOLIC DYNAMICS AND ITS APPLICATIONS, 2004, 60 : 61 - 79
12345