✦ LIBER ✦
Study of global solutions of parabolic equations via a priori estimates. Part I: Equations with principal elliptic part equal to the laplacian
✍ Scribed by Gary M. Lieberman
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 780 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We study global solutions of u~t~=Δ__u__ + f(u, D__u__) with zero boundary data. Under suitable hypotheses on f, we show that an energy, which is roughly the H^1^ norm of u, cannot change too rapidly. When f depends only on u, this estimate implies that all global solutions are bounded.