Kinetic Equations and Variational Principles
Copyright policy )Kinetic Equations and Variational Principles
The paper presents a method of symmetrization of the time-dependent neutron transport equation by which the original problem and its adjoins are reduced to one self-adjoins problem. For the latter, a variational principle based on minimization of the quadratic functional is formulated.A study is made of some properties of the problem’s operators, the proof of the existence and uniqueness of generalized solutions is presented.In the conclusion, some examples are given of the application of the formulated variational principle to developing numerical algorithms. Thus, by Ritz’s method a time-dependent diffusion elliptic-type equation with corresponding boundary conditions is derived.
variational principles, generalized solutions, Transport processes in time-dependent statistical mechanics, kinetic equations, Numerical methods for integral equations, Phase transitions (general) in equilibrium statistical mechanics, time-dependent neutron transport equation, self-adjoint problem, time-dependent diffusion elliptic- type equation, Integro-partial differential equations, radiative transport, Ritz's method, method of symmetrization
variational principles, generalized solutions, Transport processes in time-dependent statistical mechanics, kinetic equations, Numerical methods for integral equations, Phase transitions (general) in equilibrium statistical mechanics, time-dependent neutron transport equation, self-adjoint problem, time-dependent diffusion elliptic- type equation, Integro-partial differential equations, radiative transport, Ritz's method, method of symmetrization
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