论文标题
$ l^2 $ norm保存非线性热方程的存在和渐近行为
Existence and asymptotic behavior for $L^2$-norm preserving nonlinear heat equations
论文作者
论文摘要
我们考虑具有非本地术语的非线性抛物线方程，该方程可保留解决方案的$ l^2 $ norm。我们以$ h^1 $研究了有限领域以及整个欧几里得空间的本地和全球良好姿势。然后，我们研究解决方案的渐近行为。通常，我们在H^1中获得弱收敛到固定状态。对于球，当初始条件为正时，我们证明了强渐近收敛到基态。
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 asymptotic convergence to the ground state when the initial condition is positive.
