Nonlocal diffusion equations in Carnot Groups

2018/12/17 by Isolda Cardoso, Cardoso, Isolda Eugenia, Raúl E. Vidal +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1812.06911

openalex publication_date 2018/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a Carnot group. We study nonlocal diffusion equations in a domain Ω of G of the form u_t^ε(x,t)=∫_G(1)/(ε²)K_ε(x,y)(u^ε(y,t)-u^ε(x,t)) dy, x∈ Ω with u^ε=g(x,t) for x∉Ω. For appropriate rescaled kernel K_ε we prove that solutions u^ε, when ε→0, uniformly approximate the solution of different local Dirichlet problem in G. The key tool used is the Taylor series development for a function defined on a Carnot group.

Related

• Nonlocal heat equations in the Heisenberg group
• The Dirichlet problem for some nonlocal diffusion equations
• A Note on the formulation of the Neumann boundary condition for a nonlocal problem
• The diffusion equation with nonlocal data
• Nonlocal approximation of nonlinear diffusion equations