Analysis reveals decay rates of dissipative solutions in critical function spaces, suggesting insights into asymptotic behavior.
We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension d ≥ 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.
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Ikeda et al. (2025) studied this question.
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