The asymptotic behaviour of solutions of a porous medium equation with bounded measurable coefficients
In this interesting and well written paper the authors obtain the Hölder continuity of the interphases of (weak) solutions of \(u_t-\{a_{ij}(x) [u^m]_{x_i}\}_{x_j}=0 \) where \(x\in \mathbb{R}^n\), and the initial datum is assumed nonnegative, continuous and compactly supported. The matrix \([a_{ij}]\) is assumed to satisfy an ellipticity condition excluding degeneracy, having bounded and measurable coefficients. They also characterize the asymptotic behaviour of such solutions when \(t \to \infty\). The main tool is a very refined use of a weak Harnack inequality.
scientific article; zbMATH DE number 1031646