Scholarlink

In these notes, we describe the strategy for the derivation of the hydrodynamic limit for a family of long range interacting particle systems of exclusion type with symmetric rates. For \(m \in \mathbb {N}:=\{1, 2, \ldots \}\) fixed, the hydrodynamic equation is \(\partial _t \rho (t,u)= [-(-\Delta )^{\gamma /2} \rho ^m](t,u) \) . For \(m=1\) , this is the fractional equation, which is linear. On the other hand, for \(m \ge 2\) , this is the fractional porous medium equation (which is nonlinear), obtained by choosing a rate which depends on the number of particles next to the initial and final position of a jump.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Linear and Nonlinear Fractional PDEs from Interacting Particle Systems

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Pedro Cardoso,
  • Patrícia Gonçalves

摘要

In these notes, we describe the strategy for the derivation of the hydrodynamic limit for a family of long range interacting particle systems of exclusion type with symmetric rates. For \(m \in \mathbb {N}:=\{1, 2, \ldots \}\) fixed, the hydrodynamic equation is \(\partial _t \rho (t,u)= [-(-\Delta )^{\gamma /2} \rho ^m](t,u) \) . For \(m=1\) , this is the fractional equation, which is linear. On the other hand, for \(m \ge 2\) , this is the fractional porous medium equation (which is nonlinear), obtained by choosing a rate which depends on the number of particles next to the initial and final position of a jump.