Convergent Approximations in Parabolic Variationally Inequalities. I. One-Phase Stefan Problems

摘要

Many physical phenomena are modelled by inequalities rather than equations. In this report we examine a dynamic, or parabolic inequality, which characterizes the change of phase of a substance, e.g., ice melting, under certain assumptions. We obtain rates of convergence for certain approximation schemes which separately discretize time and space. The rates, as well as one of the schemes, appear to constitute new results in a subject which is still rather undeveloped. Subsequent investigations are also contemplated for inequalities related to different physical models.