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تسجيل مستخدم جديدStability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations
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The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution time-asymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain $ mathbb R times mathbb T^{n-1} (ngeq2) $, where $mathbb T^{n-1}$ is the $ n-1 $-dimensional torus.
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