We consider a nonlinear parabolic equation with a nonlocal term which preserves the L2-norm of the solution. We study the local and global well-posedness on a bounded domain, as well as the whole Euclidean space, in H1. Then we study the asymptotic behavior of solutions. In general, we obtain weak convergence in H1 to a stationary state. For a ball, we prove strong convergence to the ground state when the initial condition is positive.
Existence and asymptotic behavior for L2-norm preserving nonlinear heat equations
Antonelli, Paolo
;Shakarov, Boris
2024-01-01
Abstract
We consider a nonlinear parabolic equation with a nonlocal term which preserves the L2-norm of the solution. We study the local and global well-posedness on a bounded domain, as well as the whole Euclidean space, in H1. Then we study the asymptotic behavior of solutions. In general, we obtain weak convergence in H1 to a stationary state. For a ball, we prove strong convergence to the ground state when the initial condition is positive.File in questo prodotto:
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