Free boundary problems in partial differential equations and related topics

研究具有未知(自由)边界的非线性偏微分方程解问题。当物理系统的不同状态发生转变时，这些问题就会出现，并出现在许多数学应用中，例如在人口模型和熔化问题中，仅举两例。我们还讨论了由理解急剧转变而引发的相关问题，这在应用科学中也有许多应用。

We study problems for nonlinear partial differential equations where there is an unknown (free) boundary in the underlying domain. These problems occur when there is a transition from different states of physical systems and arise in many applications of mathematics, such as in population models and in melting problems, to mention but two. We as well discuss related problems motivated by understanding sharp transitions which also have many applications in applied sciences.