On a Doubly Nonlinear Parabolic Obstacle Problem Modelling Ice Sheet Dynamics
On a Doubly Nonlinear Parabolic Obstacle Problem Modelling Ice Sheet Dynamics
复制标题
关于冰盖动力学建模的双非线性抛物线障碍问题
DOI：
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发表时间：
2003
影响因子：
1.9
通讯作者：
C. Vázquez
中科院分区：
文献类型：
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作者：
N. Calvo;J. I. Díaz;J. Durany;E. Schiavi;C. Vázquez
本文讨论了理论冰川学中出现的自由（移动）边界问题的弱公式。考虑浅层冰盖流动，本文给出了等温条件下冰盖非牛顿动力学的二阶非线性退化抛物方程模型的数学分析和数值解。然后推导并分析了障碍物问题。用比较原理和能量法定性地描述了由解的支持所产生的自由边界的存在性和位置及其演化过程。然后用特征法和对偶算法对得到的变分不等式进行数值计算。我们引入的弱框架及其分析（定性和数值）并不局限于我们所考虑的冰盖模式的简单物理性质，也不局限于模式维度；它们可以成功地应用于与其他地球物理环境相关的更现实和更复杂的模型。
This paper deals with the weak formulation of a free (moving) boundary problem arising in theoretical glaciology. Considering shallow ice sheet flow, we present the mathematical analysis and the numerical solution of the second order nonlinear degenerate parabolic equation modelling, in the isothermal case, the ice sheet non-Newtonian dynamics. An obstacle problem is then deduced and analyzed. The existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method. Then the solutions are numerically computed with a method of characteristics and a duality algorithm to deal with the resulting variational inequalities. The weak framework we introduce and its analysis (both qualitative and numerical) are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension; they can be successfully applied to more realistic and sophisticated models related to other geophysical settings.