IUMJ

Title: The behavior of the free boundary close to a fixed boundary in a parabolic problem

Authors: D. E. Apushkinskaya, N. Matevosyan and N. N. Uraltseva

Issue: Volume 58 (2009), Issue 2, 583-604

Abstract:

A parabolic obstacle-type problem without sign restriction on the solution is considered. An exact representation of the global solutions (i.e., solutions in the entire half-space $\{(x,t)\in\mathbb{R}^{n+1}\mid x_1>0\}$) is found. Finally, the local properties of the free boundary near a fixed boundary is studied. Under the homogeneous Dirichlet condition on the given boundary, the smoothness of the free one is proved.