论文标题
一类完全非线性抛物线方程的单数诺伊曼边界问题
Singular Neumann boundary problems for a class of fully nonlinear parabolic equations in one dimension
论文作者
论文摘要
在本文中，我们讨论了一个空间维度中一类非线性抛物线方程的奇异诺伊曼边界问题。我们的边界问题描述了平面曲线沿边界滑动的运动，其接触角可以看作是毛细管现象的限制模型。我们通过使用粘度溶液理论来研究解决方案的独特性和存在。当假定初始值为凸时，我们还显示了溶液与行动波的收敛性。
In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar curve sliding along the boundary with a zero contact angle, which can be viewed as a limiting model for the capillary phenomenon. We study the uniqueness and existence of solutions by using the viscosity solution theory. We also show the convergence of the solution to a traveling wave as time proceeds to infinity when the initial value is assumed to be convex.
