On the forward in time propagation of zeros in fractional heat type problems

2023/01/28 by Agnid Banerjee, Nicola Garofalo, Banerjee, Agnid +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.12239

openalex publication_date 2023/01/28 · openalex created_date 2023/02/02 · openalex updated_date 2026/07/28

Abstract

In this short note we prove that if u solves (∂_t - Δ)^s u = Vu in \mathbb Rⁿ_x × \mathbb R_t, and vanishes to infinite order at a point (x₀, t₀), then u ≡ 0 in \mathbb Rⁿ_x × \mathbb R_t. This sharpens (and completes) our earlier result that proves u(⋅, t) ≡ 0 for t ≤ t₀ if it vanishes to infinite order at (x₀, t₀).

Related

• Decay at infinity for solutions to some fractional parabolic equations
• Fractional decay bounds for nonlocal zero order heat equations
• Quantitative uniqueness for fractional heat type operators
• Master equations with indefinite nonlinearities
• Regularity theory and extension problem for fractional nonlocal parabolic equations and the master equation