Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces

2025/12/18 by Hatano, Naoya, Ikeda, Masahiro
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.16711

Abstract

In this paper, we introduce the unconditional uniqueness of solutions in Herz spaces for the Hardy--Hénon parabolic equation, which is a semilinear heat equation with a power-type weight in the nonlinear term |x|^γ|u|^α-1u. It is expected that the power-type weight in the nonlinear term can be effectively handled within Herz spaces. In fact, our result in Herz spaces K^s_q,r(\mathbb Rⁿ) relaxes the endpoint case q=α and the large interpolation exponent case r≥ q compared to previous results.

Citations

• Asymptotically self-similar global solutions for Hardy-Hénon parabolic equations
• Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation
• Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations
• On the generalized parabolic Hardy-Hénon equation: Existence, blow-up, self-similarity and large-time asymptotic behaviour
• Optimal well-posedness and forward self-similar solution for the Hardy-Hénon parabolic equation in critical weighted Lebesgue spaces

Related

• Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations
• Well-posedness and global existence for Hardy--Hénon parabolic equations in Herz spaces
• Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation
• On the Hardy-Hénon heat equation with an inverse square potential
• Asymptotically self-similar global solutions for Hardy-Hénon parabolic equations