We consider a nonlinear parabolic equation with a nonlocal term which preserves the L-2 -norm of the solution. We study the local and global well-posedness on a bounded domain, as well as the whole Euclidean space, in H- 1. 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 convergence to the ground state when the initial condition is positive.
Antonelli, P., Cannarsa, P., Shakarov, B. (2024). Existence and asymptotic behavior for L2-norm preserving nonlinear heat equations. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 63(4) [10.1007/s00526-024-02724-6].
Existence and asymptotic behavior for L2-norm preserving nonlinear heat equations
Cannarsa P.;
2024-01-01
Abstract
We consider a nonlinear parabolic equation with a nonlocal term which preserves the L-2 -norm of the solution. We study the local and global well-posedness on a bounded domain, as well as the whole Euclidean space, in H- 1. 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 convergence to the ground state when the initial condition is positive.| File | Dimensione | Formato | |
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