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 perturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.
!!!All Science Journal Classification (ASJC) codes
- 数学 (全般)