Solvability of fractional semilinear heat equations with distributional forcing terms in Lorentz spaces
Yusuke Oka
Published: 2025/9/20
Abstract
We study the Cauchy problem for the fractional semilinear heat equation with distributional forcing terms. By using Besov-type spaces based on Lorentz spaces, we give necessary conditions and sufficient conditions on forcing terms for the local-in-time existence of solutions belonging to Lorentz spaces.