Geodesic
Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion
Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 601-612

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In this paper, we study a new class of time-periodic solutions with interior transition layer of reaction-advection-diffusion equations in the case of a fast reaction and a small diffusion. We consider the case of discontinuous sources (i.e., the nonlinearity describing the interaction and reaction) for a certain value of the unknown function that arise in a number of relevant applications. An existence theorem is proved, asymptotic approximations are constructed, and the asymptotic Lyapunov stability of such solutions as solutions of the corresponding initial-boundary-value problems is established.
Mots-clés : reaction-advection-diffusion type equations, singular perturbations
Keywords: periodic parabolic boundary-value problems, Burgers equations with modular advection, discontinuous sources, asymptotic method of differential inequalities, interior transition layer. 
@article{MZM_2022_112_4_a8,
     author = {N. N. Nefedov},
     title = {Periodic {Contrast} {Structures} in the {Reaction-Diffusion} {Problem} with {Fast} {Response} and {Weak} {Diffusion}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {601--612},
     publisher = {mathdoc},
     volume = {112},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a8/}
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N. N. Nefedov. Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion. Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 601-612. http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a8/