具有奇异数据的二维自相互作用场模型中的正则化导数
Regularized derivatives in a 2-dimensional model of self-interacting fields with singular data
摘要：
耦合麦克斯韦-洛仑兹系统描述了经典电动力学中电磁场的反馈作用。当应用于点电荷源（被视为带电流体的极限情况），所产生的非线性弱双曲系统超出了经典分布理论的范围。在广义函数的Colombeau代数的框架下，利用正则化导数，我们分析了Maxwell-Lorentz系统的二维模拟。在建立了解的存在性和唯一性之后，我们得到了关于具有$δ$样初值的解的分布极限的一些结果。
英文摘要：
The coupled Maxwell-Lorentz system describes feed-back action of electromagnetic fields in classical electrodynamics. When applied to point-charge sources (viewed as limiting cases of charged fluids) the resulting nonlinear weakly hyperbolic system lies beyond the scope of classical distribution theory. Using regularized derivatives in the framework of Colombeau algebras of generalized functions we analyze a two-dimensional analogue of the Maxwell-Lorentz system. After establishing existence and uniqueness of solutions in this setting we derive some results on distributional limits of solutions with $δ$-like initial values.
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