Optimal control of fractional Poisson equation from non-local to local

2025/03/12 by Manohar, Ram, Buda, Kedarnath, Kumar, B. V. Rathish
#$49\mathrm{J}20$ #$65\mathrm{K}10$ #$65\mathrm{N}30$ #$65\mathrm{N}50$ #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2503.09386

Abstract

In this article, the limiting behavior of the solution u_s of the optimal control problem subjected to the fractional Poisson equation (-Δ)^s u_s(x)=f_s(x), x∈ Ω defined on domain Ω bounded by smooth boundary with zero exterior boundary conditions u_s(x)≡ 0, x ∈ Ω^c is established. We will prove that lim_{s→ 1^-} u_s= u, where u is a solution of the optimal control problem subjected to classical Poisson equation -Δu(x)=f(x), x ∈ Ω and u(x)=0, x∈ ∂ Ω.

Related

• The Poisson equation from non-local to local
• Optimal control of the coefficient for fractional and regional fractional p-Laplace equations: Approximation and convergence
• External optimal control of fractional parabolic PDEs
• Differentiability of the nonlocal-to-local transition in fractional Poisson problems
• Optimal control of a parabolic fractional PDE: analysis and discretization