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

2025/09/20 by Yusuke Oka, Oka, Yusuke
Engineering · Mathematics · #35A01 #35K58 #35R11 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.16809

openalex publication_date 2025/09/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/30

Abstract

We study the Cauchy problem for the fractional semilinear heat equation with distributional inhomogeneous terms. By introducing the Lorentz--Morrey spaces, we overcome limitations of real interpolation in the classical local Morrey spaces and obtain a sharp integral estimate for the nonlinear term. Moreover, in terms of Besov-type spaces, we give necessary conditions and sufficient conditions on inhomogeneous terms for the local-in-time existence of solutions belonging to Lorentz--Morrey spaces.

Citations

• Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term
• Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces
• Fractional nonlinear heat equations and characterizations of some function spaces in terms of fractional Gauss-Weierstrass semi-groups
• Existence of solutions for time fractional semilinear parabolic equations in Besov--Morrey spaces
• Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces
• Convolution inequalities for Besov and Triebel--Lizorkin spaces, and applications to convolution semigroups
• Existence of solutions for an inhomogeneous fractional semilinear heat\n equation
• Proper inclusions of Morrey spaces
• Existence of solutions for a fractional semilinear parabolic equation with singular initial data

Related

• No local L¹ solutions for semilinear fractional heat equations
• Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces
• Existence of solutions for time fractional semilinear parabolic equations in Besov--Morrey spaces
• Fractional semilinear heat equations with singular and nondecaying initial data
• Existence of solutions for an inhomogeneous fractional semilinear heat\n equation