Existence and asymptotic behavior for $L^2$-norm preserving nonlinear heat equations
Analysis of PDEs
2025-02-28 v2
Abstract
We consider a nonlinear parabolic equation with a nonlocal term, which preserves the -norm of the solution. We study the local and global well posedness on a bounded domain, as well as the whole Euclidean space, in . Then we study the asymptotic behavior of solutions. In general, we obtain weak convergence in H^1 to a stationary state. For a ball, we prove strong asymptotic convergence to the ground state when the initial condition is positive.
Keywords
Cite
@article{arxiv.2210.04603,
title = {Existence and asymptotic behavior for $L^2$-norm preserving nonlinear heat equations},
author = {Paolo Antonelli and Piermarco Cannarsa and Boris Shakarov},
journal= {arXiv preprint arXiv:2210.04603},
year = {2025}
}