Existence of Solutions and Dynamical Models of Chandrasekhar H-Equations

J. Chen, W. Greenberg and R. L. Bowden
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W. Greenberg: Center for Transport Theory & Mathematical Physics Virginia Tech
R. L. Bowden: Center for Transport Theory & Mathematical Physics Virginia Tech

A chapter in Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media, 1999, pp 51-69 from Springer

Abstract: Abstract A variety of linear transport equations may be solved in terms of a scattering function,which itself is expressible as a product of so-called H-functions.These functions,first introduced by S. Chandrasekhar [1],satisfy nonlinear integral equations of the form 1 $$H\left( \mu \right) = 1 + \mu H\left( \mu \right)\int_0^1 {\frac{{\psi \left( {\mu '} \right)}}{{\mu + \mu '}}H\left( {\mu '} \right)d\mu '} ,$$ where ß/i(µ) is a characteristic function. It is well known that this equation does not have a unique solution. However, the physical solution of (1) is subject to constraints at the zeroes of the dispersion function. Chandrasekhar [2] provided a solution formula with constants depending upon the roots of a characteristic equation,although such roots are difficult to calculate.

Keywords: Periodic Orbit; Bifurcation Point; Periodic Point; Invariant Manifold; Dimensional System (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4615-4799-0_3

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