Geodesic
Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities
Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 1, pp. 137-153 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence of stationary solutions of singularly perturbed systems of reaction–diffusion–advection equations is studied in the case of fast and slow reaction–diffusion–advection equations with nonlinearities containing the gradient of the squared sought function (KPZ nonlinearities). The asymptotic method of differential inequalities is used to prove the existence theorems. The boundary layer asymptotics of solutions are constructed in the case of Neumann and Dirichlet boundary conditions. The case of quasimonotone sources and systems without the quasimonotonicity requirement is also considered.
Mots-clés : singular perturbation, reaction–diffusion–advection equations
Keywords: stationary solutions, KPZ nonlinearities, asymptotic method of differential inequalities, boundary layer, Lyapunov stability. 
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     title = {Existence and stability of stationary solutions with boundary layers in a~system of fast and slow reaction{\textendash}diffusion{\textendash}advection equations with {KPZ} nonlinearities},
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N. N. Nefedov; A. O. Orlov. Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities. Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 1, pp. 137-153. http://geodesic.mathdoc.fr/item/TMF_2024_220_1_a8/

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