Paraboli - Study guides, Class notes & Summaries

In this note, we consider bounded local weak solutions u ∈ C([0, +∞) : L 1 (Ω)) ∩ L∞(Ω × (0, +∞)) of the nonlinear diffusion (sometimes called as porous media) equation ( ∂u ∂t = ∆(|u| m−1 u) and |u| ≤ M in Ω × (0, +∞), u(x, 0) = u0(x) on Ω, (1) where Ω ⊂ R N is an open set (not necessarily bounded), m > 1, M > 0 and u0(x) is a bounded function. For the sake of the exposition we shall assume that u and u0 are nonnegative functions. Thus |u| ...

Finding all square roots of a number | Graphing a paraboli of the form y = ax² | Graph the parabola y = ax²