论文标题
极地FIRN气体扩散的直接和反问题
Direct and Inverse Problem for Gas Diffusion in Polar Firn
论文作者
论文摘要
事实证明，同时使用部分微分方程与数据分析结合使用是一种有效的方法，可以在不同领域（例如医学，生物学和生态学）中获得各种现象的主要参数。在生态领域，对过去几个世纪的气候变化（包括全球变暖）的研究需要估计大气中的气体浓度不同，主要是CO2。在[12、15、16、17]中得出了深极冰（FIRN）中气体捕获的数学模型，该模型由抛物线偏微分方程组成，该方程在一个边界极端几乎是变性的。在本文中，我们将所有系数视为常数，除了要重建的扩散系数。我们介绍了这种直接问题的存在，独特性和模拟的理论方面，并因此提出了试图使用给定生成的数据来恢复扩散系数的反问题。
Simultaneous use of partial differential equations in conjunction with data analysis has proven to be an efficient way to obtain the main parameters of various phenomena in different areas, such as medical, biological, and ecological. In the ecological field, the study of climate change (including global warming) over the past centuries requires estimating different gas concentrations in the atmosphere, mainly CO2. The mathematical model of gas trapping in deep polar ice (Firns) has been derived in [12, 15, 16, 17], consisting of a parabolic partial differential equation that is almost degenerate at one boundary extreme. In this paper, we consider all the coefficients to be constants, except the diffusion coefficient that is to be reconstructed. We present the theoretical aspects of existence, uniqueness and simulation for such direct problem and consequently formulate the inverse problem that attempts at recovering the diffusion coefficients using given generated data
