Geodesic
On the nature of local equilibrium in the Carleman and Godunov--Sultangazin equations
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, Tome 60 (2016), pp. 23-81

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Considering one-dimensional Carleman and Godunov–Sultangazin equations, we obtain the local equilibrium conditions for solutions of the Cauchy problem with finite energy and periodic initial data. Moreover, we prove the exponential stabilization to the equilibrium state. 
@article{CMFD_2016_60_a1,
     author = {O. A. Vasil'eva and S. A. Dukhnovskii and E. V. Radkevich},
     title = {On the nature of local equilibrium in the {Carleman} and {Godunov--Sultangazin} equations},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {23--81},
     publisher = {mathdoc},
     volume = {60},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_60_a1/}
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O. A. Vasil'eva; S. A. Dukhnovskii; E. V. Radkevich. On the nature of local equilibrium in the Carleman and Godunov--Sultangazin equations. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, Tome 60 (2016), pp. 23-81. http://geodesic.mathdoc.fr/item/CMFD_2016_60_a1/