Inverse Problems for Drift-Diffusion Equations with Applications to Chemotaxis and Synthetic Nanopores

漂移扩散方程反问题及其在趋化性和合成纳米孔中的应用

• 批准号: 222235984
• 负责人: Professor Dr. Jan-Frederik Pietschmann
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/222235984?language=en
• 关键词: Inverse; Problems; Drift; Diffusion; Equations

In this renewal proposal we consider questions related to inverse problems of nonlinear drift--diffusion equations and systems thereof. One focus is the treatment of chemotaxis, defined as the directed movement of cells along the gradient of a chemical substance. This is modelled by equations featuring unknown nonlinear functions which we aim to reconstruct given measurements of the cell density. We also treat the problem of stable reconstruction of these functions and the analysis of numerical schemes which allow the application to real data. An additional aspect is the treatment of lower order terms as well as the usage of nonlinear boundary conditions. Finally, we consider the modelling, simulation and optimisation of synthetic nanopores.

在这个更新方案中，我们考虑了与非线性漂移-扩散方程及其方程组的反问题有关的问题。一个焦点是趋化性的治疗，趋化性的定义是细胞沿着化学物质的梯度定向移动。这是由具有未知非线性函数的方程建模的，我们的目标是重建给定的细胞密度测量结果。我们还讨论了这些函数的稳定重构问题和允许应用于真实数据的数值格式的分析。另一个方面是低阶项的处理以及非线性边界条件的使用。最后，我们考虑了合成纳米孔的建模、模拟和优化。

项目成果

Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales

通过希尔伯特尺度正则化非线性扩散定律的数值识别

• DOI: 10.1088/0266-5611/30/2/025004
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: H. Egger;J.-F. Pietschmann;M. Schlottbom
• 通讯作者: M. Schlottbom

Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem

拟线性椭圆问题中扩散系数和吸收系数的同时识别

• DOI: 10.1088/0266-5611/30/3/035009
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: H. Egger;J.-F. Pietschmann;M. Schlottbom
• 通讯作者: M. Schlottbom

Flow characteristics in a crowded transport model

拥挤运输模型中的流动特性

• DOI: 10.1088/0951-7715/29/11/3528
• 期刊: Nonlinearity
• 影响因子: 1.7
• 作者: M. Burger;J.-F. Pietschmann
• 通讯作者: J.-F. Pietschmann

On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion

具有非局部相互作用和尺寸排除的多个物种的交叉扩散模型

• DOI: 10.1016/j.na.2017.03.010
• 期刊: arXiv: Analysis of PDEs
• 作者: J. Berendsen;M. Burger;J.-F. Pietschmann
• 通讯作者: J.-F. Pietschmann

Asymptotic models for transport in large aspect ratio nanopores

大纵横比纳米孔传输的渐近模型

• DOI: 10.1017/s0956792518000293
• 期刊: European Journal of Applied Mathematics
• 影响因子: 1.9
• 作者: B. Matejczyk;J.-F. Pietschmann;G. Richardson;M.T. Wolfram
• 通讯作者: M.T. Wolfram