Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow
Analysis of PDEs
2024-11-28 v1
Abstract
We consider a nonlinear parabolic model that forces solutions to stay on a -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.
Cite
@article{arxiv.2411.18532,
title = {Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow},
author = {Boris Shakarov},
journal= {arXiv preprint arXiv:2411.18532},
year = {2024}
}