https://doi.org/10.1051/epjconf/201922401005
Asymptotic Time-Behaviour of Solutions to Scalar Conservation Law with a Convex Flux Function
Moscow State Technological University “STANKIN”, RU-127055, Moscow, Russia
* e-mail: petrossian55@mail.ru
Published online: 9 December 2019
We consider the long-time behaviour of solutions of the Cauchy problem for a quasilinear equation ut + f(u)x = 0 with a strictly convex flux function f(u) and initial function u0(x) having the the one-sided limiting mean values u± that are uniform with respect to translations. The estimates of the rates of convergence to solutions of the Riemann problem depending on the behaviour of the integrals 
as y→±∞ are established. The similar results are obtained for solutions of the mixed problem in the domain x > 0, t > 0 with a constant boundary data u– and initial data having limiting mean value u±.
© The Authors, published by EDP Sciences, 2019
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