论文标题
在动态边界条件的扰动快速扩散方程
On a perturbed fast diffusion equation with dynamic boundary conditions
论文作者
论文摘要
本文讨论了具有动态边界条件的扰动快速扩散方程的有限时间灭绝。快速扩散方程具有衰减的特征属性，例如，根据初始数据，溶液衰减在有限的时间内为零。在目标问题中，大约$ p $ - th或$ q $ - 订单的扰动项可能会在此期间爆炸。问题是由于扩散与爆炸之间的冲突引起的，在散装和边界上。首先，获得溶液的局部存在和独特性。最后，提出了一些小初始数据的有限时间灭绝的结果。
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite amount of time depending upon the initial data. In the target problem, some $p$-th or $q$-th order perturbation term may work to blow up within this period. The problem arises from the conflict between the diffusion and the blow up, in the bulk and on the boundary. Firstly, the local existence and uniqueness of the solution are obtained. Finally, a result of finite time extinction for some small initial data is presented.
