Universal bounds for global solutions of nonlinear parabolic equations

• Published in: Нелинейные граничные задачи
• Date: 2002
• Main Author: Fila, M.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2002
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/169228
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Universal bounds for global solutions of nonlinear parabolic equations / M. Fila // Нелинейные граничные задачи. — 2002. — Т. 12. — С. 179-188. — Бібліогр.: 14 назв. — англ.

In this survey we consider parabolic problems for which blow-up in finite time occurs for some initial data but global positive solutions may also exist. We present results on universal L∞-bounds for global positive solutions. These bounds will be of the form u(x,t) ≤ C(τ), x ∊ Ω t ≥ τ ›0, where C(...