Nogueira, Ariadne; Nakasato, Jean Carlos; Pereira, Marcone Corrêa Concentrated reaction terms on the boundary of rough domains for a quasilinear equation. (English) Zbl 1440.35008 Appl. Math. Lett. 102, Article ID 106120, 7 p. (2020). Summary: In this work we analyze the solutions of a \(p\)-Laplacian equation with homogeneous Neumann boundary conditions set in a family of rough domains with a nonlinear term concentrated on the boundary. At the limit, we get a nonlinear boundary condition capturing the oscillatory geometry of the strip where the reactions take place. Cited in 4 Documents MSC: 35B25 Singular perturbations in context of PDEs 35J25 Boundary value problems for second-order elliptic equations 35J92 Quasilinear elliptic equations with \(p\)-Laplacian Keywords:\(p\)-Laplacian; Neumann problem; oscillating domains; asymptotic analysis; concentrated reactions PDFBibTeX XMLCite \textit{A. Nogueira} et al., Appl. Math. Lett. 102, Article ID 106120, 7 p. (2020; Zbl 1440.35008) Full Text: DOI arXiv References: [1] Aragão, G. S.; Pereira, A. L.; Pereira, M. C., A nonlinear elliptic problem with terms concentrating in the boundary, Math. Methods Appl. Sci., 35, 1110-1116 (2012) · Zbl 1252.35029 [2] Aragão, G. S.; Pereira, A. L.; Pereira, M. C., Continuity of attractors for a nonlinear parabolic problem with terms concentrating in the boundary, J. Dynam. Differential Equations, 26, 4, 871-888 (2014) · Zbl 1335.35150 [3] Arrieta, J. M.; Jiménez-Casas, A.; Rodríguez-Bernal, A., Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary, Rev. Mat. Iberoamericana, 24, 183-211 (2008) · Zbl 1162.35021 [4] Aragão, G. S.; Bruschi, S., Concentrated terms and varying domains in elliptic equations: Lipschitz case, Math. Methods Appl. Sci., 39, 3450-3460 (2016) · Zbl 1345.35035 [5] Arrieta, J. M.; Carvalho, A. N., Spectral convergence and nonlinear dynamics for reaction-diffusion equations under perturbations of the domain, J. Differential Equations, 199, 143-178 (2004) · Zbl 1058.35028 [6] Arrieta, J. M.; Nogueira, A.; Pereira, M. C., Nonlinear elliptic equations with concentrating reaction terms at an oscillatory boundary, Discrete Contin. Dyn. Syst. B, 24, 8, 4217-4246 (2019) · Zbl 1429.35090 [7] Chechkin, G.; Friedman, A.; Piatnistski, A., The boundary-value problem in domains with very rapidly oscillating boundary, J. Math. Anal. Appl., 231, 213-234 (1999) · Zbl 0938.35049 [8] Arrieta, J. M.; Nogueira, A.; Pereira, M. C., Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries, Comput. Math. Appl., 77, 536-554 (2019) · Zbl 1442.35155 [9] Grisvard, P., Elliptic Problems in Nonsmooth Domains (2011), Society for Industrial and Applied Mathematics · Zbl 1231.35002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.