Semilinear elliptic equations in thin regions with terms concentrating\n on oscillatory boundaries

2018/03/25 by José M. Arrieta, Arrieta, José M., Ariadne Nogueira +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1803.09345

openalex publication_date 2018/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we study the behavior of a family of solutions of a semilinear\nelliptic equation, with homogeneous Neumann boundary condition, posed in a\ntwo-dimensional oscillating thin region with reaction terms concentrated in a\nneighborhood of the oscillatory boundary. Our main result is concerned with the\nupper and lower semicontinuity of the set of solutions. We show that the\nsolutions of our perturbed equation can be approximated with ones of a\none-dimensional equation, which also captures the effects of all relevant\nphysical processes that take place in the original problem.\n

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