Convergence to nonlinear diffusion waves for solutions of Euler-Korteweg equations with damping

Journal of Evolution Equations - Tập 18 - Trang 29-47 - 2017
Haibo Cui1, Jing Du1
1School of Mathematical Sciences, Huaqiao University, Quanzhou, People’s Republic of China

Tóm tắt

In this paper, we are concerned with the asymptotic behavior of solutions to Euler-Korteweg equations with damping. We prove that the solutions time-asymptotically behave like the nonlinear diffusion wave, as in Hsiao and Liu (Commun Math Phys 143:599–605, 1992) and Nishihara (J Differ Equ 131:171–188, 1996). Moreover, it is also shown that the Euler-Korteweg equations with damping could be a approximation of the Euler equations with damping.

Tài liệu tham khảo

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