We study some extremal properties of the self-similar solutions of certain onedimensional kinetic models of granular flows, usually known with the name of nonlinear friction equations. This analysis, inspired by some recent results on nonlinear diffusion equations [6], allows to obtain various sharp inequalities, which can be fruitfully used to better clarify the large-time behavior of the solution density.
Sharp cooling rates in nonlinear friction equations / G. Furioli, A. Pulvirenti, E. Terraneo. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 27:1(2016), pp. 127-146.
Sharp cooling rates in nonlinear friction equations
E. TerraneoUltimo
2016
Abstract
We study some extremal properties of the self-similar solutions of certain onedimensional kinetic models of granular flows, usually known with the name of nonlinear friction equations. This analysis, inspired by some recent results on nonlinear diffusion equations [6], allows to obtain various sharp inequalities, which can be fruitfully used to better clarify the large-time behavior of the solution density.
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