This paper is concerned with the asymptotic behavior toward the rarefaction wave uR(x/t) of the solution of the Burgers equation with viscosity. If the initial data are suitably close to constant state u± at x=±∞, then the solution u(x, t), roughly speaking, satisfies supR |u -uR| ∼t-1/2 as t → ∞ and, except for the "neighborhoods" of the corners, x=u±t of uR, sup |u-uR|∼t-1. In the proof the exact forms of u are available.
|ジャーナル||Japan Journal of Industrial and Applied Mathematics|
|出版ステータス||Published - 1991 2|
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