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Bibliographic Details
Main Author: Shakarov, Boris
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2411.18532
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Table of Contents:
  • We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy space. Then, we consider the solutions' asymptotic behavior. We prove strong convergence to a stationary state and asymptotic convergence to the ground state in bounded domains when the initial condition is positive.