On a perturbed fast diffusion equation with dynamic boundary conditions
On a perturbed fast diffusion equation with dynamic boundary conditions
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发表时间：
2020-09
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通讯作者：
T. Fukao
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作者：
T. Fukao
讨论了一类带动力边界条件的快扩散方程的有限时间绝灭问题。快速扩散方程具有衰减的特性，例如解在有限时间内衰减到零，这取决于初始数据。在目标问题中，某些p阶或q阶扰动项可能在此期间内爆破。这个问题是由扩散和爆破之间的冲突，在体积和边界上。首先，得到了解的局部存在唯一性。最后给出了小初值条件下有限时间灭绝的一个结果。
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.