2012/05/23 by Alexander Kolpakov, Kolpakov, A. A., A. G. Kolpakov +1 · 1 citation
Mathematics · #35Q70 #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1205.5157
openalex publication_date 2012/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an interaction of charged bodies under the following simplified conditions: the distribution of charge over each body is stable; the interaction of bodies is governed by electrical forces only. Physically, these assumptions can be treated as the following decomposition of charges: the structure of each body is assumed to be stable due to inner forces (say, quantum forces [1]), which do not influence the interaction of the bodies; the bodies interact due to the classical electrical forces [2] only. In this model, the role of inner forces is to create a specific stable distribution of the charge over a body. We assume that the charge distribution over a body can be described by the density of the charge. In our model, the distribution of the charge is the property of a body and does not change in the process of the bodies' interaction. For the simplicity we assume that the bodies are similar in the sense of geometry, say, occupy domain Q and have a preferable direction of interaction denoted by Ox3.