Fractional nonlinear heat equations and characterizations of some function spaces in terms of fractional Gauss-Weierstrass semi-groups

2024/02/09 by Franka Baaske, Baaske, Franka, Hans‐Jürgen Schmeißer +3 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2402.06309

openalex publication_date 2024/02/09 · openalex created_date 2024/02/13 · openalex updated_date 2026/07/28

Abstract

We present a new proof of the caloric smoothing related to the fractional Gauss-Weierstrass semi-group in Triebel-Lizorkin spaces. This property will be used to prove existence and uniqueness of mild and strong solutions of the Cauchy problem for a fractional nonlinear heat equation.

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• Solvability of inhomogeneous fractional semilinear heat equations in Lorentz--Morrey spaces

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