251 citations
- Siberian Federal UniversityRU42 papers
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5 papers · 1 filter
The additive generalization of the Boltzmann entropy
Alexander N. Gorban, Iliya V. Karlin, Hans Christian Ottinger
There exists only one generalization of the classical Boltzmann-Gibbs-Shannon entropy functional to a one-parametric family of additive entropy functionals. We find analytical solu…
Hydrodynamics from Grad's equations: What can we learn from exact solutions?
Iliya V. Karlin, Alexander N. Gorban
A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal…
Method of invariant manifold for chemical kinetics
Alexander N. Gorban, Iliya V. Karlin
In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant mani…
Family of additive entropy functions out of thermodynamic limit
Alexander N. Gorban, Iliya V. Karlin
Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description…
Differential constraints and exact solutions of nonlinear diffusion equations
Oleg V. Kaptsov, Igor V. Verevkin
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such d…