<!--StartFragment -->Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation<!--EndFragment -->

Dynamics of Partial Differential Equations 2026 Open access

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Authors: Masahiro Ikeda, César J. Niche, Gabriela Del Valle Planas
DOI: 10.4310/dpde.260103060355
Cited by: 0

Abstract

We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension $d \geq 5$. By employing the Fourier splitting method, we establish precise decay rates for dissipative solutions, meaning those whose critical norm vanishes as time approaches infinity. Our findings offer a deeper understanding of the asymptotic properties and dissipation mechanisms governing this equation.

Fields of Study & Subjects

Advanced Mathematical Physics Problems Stability and Controllability of Differential Equations

Publication details

Journal / source
Dynamics of Partial Differential Equations
Volume
23
Issue
1
Pages
1–18
Publication date
1 January 2026
Language
EN