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January 2020 Global asymptotics toward the rarefaction waves for solutions to the Cauchy problem of the scalar conservation law with nonlinear viscosity
Akitaka Matsumura, Natsumi Yoshida
Osaka J. Math. 57(1): 187-205 (January 2020).

Abstract

In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.

Citation

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Akitaka Matsumura. Natsumi Yoshida. "Global asymptotics toward the rarefaction waves for solutions to the Cauchy problem of the scalar conservation law with nonlinear viscosity." Osaka J. Math. 57 (1) 187 - 205, January 2020.

Information

Published: January 2020
First available in Project Euclid: 15 January 2020

zbMATH: 07196623
MathSciNet: MR4052636

Subjects:
Primary: 35B40, 35K55, 35L65

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

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Vol.57 • No. 1 • January 2020
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