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arXiv · 2504.08265

Qualitative properties of solutions to a fractional pseudo-parabolic equation with singular potential

Xiang-kun Shao·Nan-jing Huang·Xue-song Li
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Abstract

This paper investigates the initial boundary value problem for a fractional pseudo-parabolic equation with singular potential. The global existence and blow-up of solutions to the initial boundary value problem are obtained at low initial energy. Moreover, the exponential decay estimates for global solutions and energy functional are further derived, and the upper and lower bounds of both blow-up time and blow-up rate for blow-up solutions are respectively estimated. Specifically, we extend the method for proving blow-up of solutions with negative initial energy in previous literatures to cases involving nonnegative initial energy, which broadens the applicability of this method. Finally, for the corresponding stationary problem, the existence of ground-state solutions is established, and it is proved that the global solutions strongly converge to the solutions of stationary problem as time tends to infinity.

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Xiang-kun Shao, Nan-jing Huang, Xue-song Li. 2025-04-11. Qualitative properties of solutions to a fractional pseudo-parabolic equation with singular potential. https://arxiv.org/abs/2504.08265

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