涉及相互作用边界层与内部层的对流-扩散方程的渐近分析
偏微分方程分析
2020-07-15 v1
摘要
当 ε \varepsilon ε y t ε − ε y x x ε + M y x ε = 0 y^{\varepsilon}_t-\varepsilon y^{\varepsilon}_{xx} + M y^{\varepsilon}_x=0 y t ε − ε y xx ε + M y x ε = 0 ( x , t ) ∈ ( 0 , 1 ) × ( 0 , T ) (x,t)\in (0,1)\times (0,T) ( x , t ) ∈ ( 0 , 1 ) × ( 0 , T ) O ( ε ) \mathcal{O}(\varepsilon) O ( ε ) O ( ε ) \mathcal{O}(\sqrt{\varepsilon}) O ( ε ) T T T y ε y^{\varepsilon} y ε y ε y^\varepsilon y ε P ~ ε \widetilde{P}^\varepsilon P ε ε \varepsilon ε ∥ y ε − P ~ ε ∥ L ∞ ( 0 , T ; L 2 ( 0 , 1 ) ) = O ( ε 3 / 2 ) \Vert y^{\varepsilon}-\widetilde{P}^\varepsilon\Vert_{L^\infty(0,T; L^2(0,1))}=\mathcal{O}(\varepsilon^{3/2}) ∥ y ε − P ε ∥ L ∞ ( 0 , T ; L 2 ( 0 , 1 )) = O ( ε 3/2 ) ∥ y ε − P ~ ε ∥ L 2 ( 0 , T ; H 1 ( 0 , 1 ) ) = O ( ε ) \Vert y^{\varepsilon}-\widetilde{P}^\varepsilon\Vert_{L^2(0,T; H^1(0,1))}=\mathcal{O}(\varepsilon) ∥ y ε − P ε ∥ L 2 ( 0 , T ; H 1 ( 0 , 1 )) = O ( ε )
引用
@article{arxiv.1904.12669,
title = {Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers},
author = {Youcef Amirat and Arnaud Munch},
journal= {arXiv preprint arXiv:1904.12669},
year = {2020}
}