Universal bounds for global solutions of nonlinear parabolic equations

Abstract

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(τ ) › 0 does not depend on initial data.