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arXiv · 1909.02805

The Stability of the Solutions for a Quasilinear Degenerate Parabolic Equation

Miao Ouyang·Huashui Zhan
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Abstract

The equation arising from Prandtl boundary layer theory is considered. The existence of the entropy solution can be proved by BV estimate method. The interesting problem is that, since a may be degenerate on the boundary, the usual boundary value condition may be overdetermined. Accordingly, only dependent on a partial boundary value condition, the stability of solutions can be expected. This expectation is turned to reality by Kruzkov's bi-variables method, a reasonable partial boundary value condition matching up with the equation is found first time. Moreover, the stability can be proved even without any boundary value condition.

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Miao Ouyang, Huashui Zhan. 2019-09-06. The Stability of the Solutions for a Quasilinear Degenerate Parabolic Equation. https://arxiv.org/abs/1909.02805

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