抛物型偏微分方程系统两相Stefan问题的弱解存在性
Existence of weak solutions to two-phase Stefan problems for parabolic partial differential equation system
浏览论文内容
中文总结 AI 辅助
本文针对面包烘焙过程的两相Stefan问题，在放宽初始函数条件后，证明了弱解的存在性，弥补了强解仅适用于严格条件下的局限。
中文摘要 AI 辅助
在我们之前的结果中，我们提出了一个描述热烤箱中面包烘焙过程的新自由边界问题。该问题由内能和水分质量的守恒定律、Stefan条件、边界条件和初始条件组成。我们注意到，水分含量的边界条件包含边界处的温度。因此，我们不期望$W^{1,2}$-初始数据存在强解。为了解决这一困难，我们在文献[3]中通过假设初始函数满足更严格的条件建立了强可解性。相比之下，本文旨在证明当这些对初始函数的假设被放宽时，弱解的存在性。
英文摘要
In our previous results, we have proposed a new free boundary problem representing the bread baking process in a hot oven. The problem consists of conservation laws for the internal energy and water mass, the Stefan condition, the boundary and initial conditions. We note that the boundary condition for the water content contains the temperature at the boundary. Accordingly, we do not expect a strong solution for $W^{1,2}$-initial data. To address this difficulty, we established strong solvability by assuming stricter conditions for the initial functions in [3]. In contrast, this paper aims to prove the existence of a weak solution, when these assumptions for initial functions are relaxed.
