Asymptotic behaviour for the Fractional Heat Equation in the Euclidean\n space

2017/08/01 by Vázquez, Juan Luis · 2 citations
Mathematics · #35B40 #35K55 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1708.00821

openalex publication_date 2017/08/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We consider weak solutions of the fractional heat equation posed in the whole\nn-dimensional space, and establish their asymptotic convergence to the\nfundamental solution as t\→\∞ under the assumption that the initial\ndatum is an integrable function, or a finite Radon measure. Convergence with\nsuitable rates is obtained for solutions with a finite first initial moment,\nwhile for solutions with compactly supported initial data convergence in\nrelative error holds. The results are applied to the fractional Fokker-Planck\nequation. Brief mention of other techniques and related equations is made.\n

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