Three-Dimensional Stationary Spherically Symmetric Stellar Dynamic Models Depending on the Local Energy
نویسندگان
چکیده
The stellar dynamic models considered here deal with triples ( $$f,\;\rho ,\;U$$ ) of three functions: the distribution function $$f = f(r,u)$$ , local density $$\rho \rho (r)$$ and Newtonian potential $$U U(r)$$ where $$r: \left| x \right|$$ $$u: {v} $$(x,{v}) \in {{\mathbb{R}}^{3}} \times {{\mathbb{R}}^{3}}$$ are space-velocity coordinates), $$f$$ is a $$q$$ energy $$E U(r) + \frac{{{{u}^{2}}}}{2}$$ . Our first result an answer to following question: Given (positive) $$p p(r)$$ on bounded interval $$[0,R]$$ how can one recognize $$p$$ as model given type (“inverse problem”)? If this case, we say that “extendable” (to complete model). Assuming strictly decreasing reveal connection between $$F$$ which appears in nonlinear integral equation FU[p]$$ solvability Eddington’s (Theorem 4.1). Second, investigate question (“direct problem”): Which induce functions form q( - E(r,u) {{E}_{0}})$$ model? This leads investigation approximative constructive way by mainly numerical methods.
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ژورنال
عنوان ژورنال: Computational Mathematics and Mathematical Physics
سال: 2022
ISSN: ['1555-6662', '0965-5425']
DOI: https://doi.org/10.1134/s0965542522090081