Abstract: The report is devoted to description of propagation of oscillations in solutions of scalar conservation laws provided with initial oscillatory data. The kinetic formulation of scalar conservation laws is introduced and the bound on the noisiness function is established. This bound is the main result of the present work. The noisiness function characterizes intensity of oscillations, in a sense. As a byproduct, we construct a new proof of the uniqueness theorem for entropy solutions to the Cauchy problem.

Cite: Sazhenkov S.A.
Noisiness estimate for kinetic solutions of scalar conservation laws
“Ломоносовские чтения на Алтае: фундаментальные проблемы науки и техники” - 2018 13-16 Nov 2018