论文标题
在有限域中某些快速扩散方程的冒泡和灭绝
Bubbling and extinction for some fast diffusion equations in bounded domains
论文作者
论文摘要
我们研究具有Brezis-Nirenberg效应的有限域中的Sobolev临界快速扩散方程。我们获得其阳性溶液的消光轮廓，并表明常规规范中相对误差的收敛速率至少是多项式的。通用域证明了指数衰减率。我们的证明利用了其规律性估计，曲率类型的演变方程以及爆炸分析。还获得了Sobolev亚临界快速扩散方程的结果。
We study a Sobolev critical fast diffusion equation in bounded domains with the Brezis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the convergence rates of the relative error in regular norms are at least polynomial. Exponential decay rates are proved for generic domains. Our proof makes use of its regularity estimates, a curvature type evolution equation, as well as blow up analysis. Results for Sobolev subcritical fast diffusion equations are also obtained.
