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Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law

Yoshida Natsumi

Journal of Applied Analysis

2023

Vol. 29, nr 2

251--259

In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation law where the far field constant state is prescribed. We prove that the solution of the Cauchy problem tends toward the constant state as time goes to infinity.