Mathematical modelling and analysis of nanoparticle gradients induced by magnetic fields

作者：Himmel**ach Dominik; Neuss Radu Maria^*; NeuSS Nicolas

来源：Journal of Mathematical Analysis and Applications, 2018, 461(2): 1544-1560.

DOI：10.1016/j.jmaa.2017.12.026

• Magnetic field
• Superparamagnetic nanoparticle
• Magnetic targeting
• Quasilinear parabolic equations
• Radially symmetrical solution

In this paper, we derive mathematical models for the dynamics of superparamagnetic nanoparticles under the influence of applied magnetic fields. Such models are needed in many applications, e.g. magnetic drug targeting in cancer therapy. They are the starting point for the development of stable numerical approaches and for the formulation of optimization problems, which are needed for the optimal design of magnetic field configurations. Furthermore, we show the existence and uniqueness of classical radially symmetrical solutions and illustrate their qualitative behaviour by numerical simulations using Matlab.

• 出版日期2018-5-15