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GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY

Matsumura, Akitaka 大阪大学 DOI:10.18910/73745

2020.01

概要

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. ...

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Akitaka Matsumura

Department of Pure and Applied Mathematics

Graduate School of Information Science and Technology

Osaka University, Suita, Osaka 565–0871

Japan

e-mail: akitaka@math.sci.osaka-u.ac.jp

Natsumi Yoshida

OIC Research Organization

Ritsumeikan University, Ibaraki, Osaka 567–8570

Japan

email: 14v00067@gst.ritsumei.ac.jp

[Current Address:]

Faculty of Culture and Information Science

Doshisha University, Kyotanabe, Kyoto 610–0394

Japan

e-mail: jt-bnk68@mail.doshisha.ac.jp

...

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