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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2020

Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers

Résumé

As ε goes to zero, the unique solution of the scalar advection-diffusion equation y ε t −εy ε xx +M y ε x = 0, (x, t) ∈ (0, 1) × (0, T) submitted to Dirichlet boundary conditions exhibits a boundary layer of size O(ε) and an internal layer of size O(√ ε). If the time T is large enough, these thin layers where the solution y ε displays rapid variations intersect and interact each other. Using the method of matched asymptotic expansions, we show how we can construct an explicit approximation P ε of the solution y ε satisfying y ε − P ε L ∞ (0,T ;L 2 (0,1)) = O(ε 3/2) and y ε − P ε L 2 (0,T ;H 1 (0,1)) = O(ε), for all ε small enough.
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Dates et versions

hal-02110729 , version 1 (25-04-2019)
hal-02110729 , version 2 (23-10-2020)

Identifiants

Citer

Youcef Amirat, Arnaud Munch. Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers. Mathematical Methods in the Applied Sciences, 2020, 43 (11), pp.6823-6860. ⟨10.1002/mma.6425⟩. ⟨hal-02110729v2⟩
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