The existence of time local C∞-solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the "L∞-energy method" developed in our previous paper  and a new method based on the theory of evolution equations in the L2-framework which enables us to handle with porturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.
|ジャーナル||Journal of the Mathematical Society of Japan|
|出版ステータス||Published - 2001 10月|
ASJC Scopus subject areas
- 数学 (全般)