一类快扩散方程解的消失及衰减估计

Extinction and Decay Estimate of the Solutions for a Class of Fast Diffusion Equations

利用积分模估计的方法研究一维与二维情形中快扩散方程解的消失现象。研究过程中巧妙利用低维空间中的Sobolev嵌入不等式和Hlder不等式得出解发生消失的充分条件及其衰退估计。特别是,临界情形时解的消失行为依赖于拉普拉斯算子的第一特征值。

In this paper, we investigate extinction of solutions for the fast diffusion equations by using integral norm estimate method, and we use Sobolev imbedding inequality and H lder＇s inequality to find the sufficient condition for the existence of extinction solution and its decay estimates. In particular, the extinction behaviour of solutions depend on the first eigenvalues of Laplacian operator in the critical case.