| Alain Haraux†, Rafael Ortega‡
Abstract: The usual equation for the motion of electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear, mainly a contraction of orbits for large time. A special model is studied in which the dissipation coefficient varies as the inverse of the square of the distance to the nucleus, and it is shown that this equation has contraction properties similar to the case of a linear damping, but the backward equation shows affine growth of the orbits for large time, which is more realistic than the exponential growth in the case of linear damping. Keywords: gravitation, singular potential, second order differential equation, global solutions, asymptotic bounds. MSC: 34A34, 34C11, 34D05. DOI 10.56082/annalsarscimath.2026.2.65 †alain.haraux@sorbonne-universite.fr, Sorbonne Université, Université Paris Diderot SPC, CNRS, INRIA, Laboratoire Jacques-Louis Lions, LJLL, F-75005, Paris, France |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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