2022/03/24 by Vedansh Arya, Arya, Vedansh, Agnid Banerjee +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2203.13141
openalex publication_date 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we obtain quantitative bounds on the maximal order of vanishing for solutions to (∂t - Δ)s u =Vu for s∈ [1/2, 1) via new Carleman estimates. Our main result Theorem 1.1 and Theorem 1.3 can be thought of as a parabolic generalization of the corresponding quantitative uniqueness result in the time independent case due to Rüland and it can also be regarded as a nonlocal generalization of a similar result due to Zhu for solutions to local parabolic equations.