Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries

Author(s)

Nakasato, Jean Carlos ; Pereira, Marcone Correa

• Document type: Journal article
• Source: ADVANCED NONLINEAR STUDIES; v. 23, n. 1, p. 38-pg., 2023-08-29.

Abstract

In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating (N+ 1)-dimensional thin domains (i.e., a family of bounded open sets from RN+ 1, with corrugated bounder, which degenerates to an open bounded set in R-N). We also allow monotone nonlinear boundary conditions on the rough border whose magnitude depends on the squeezing of the domain. According to the intensity of the roughness and a reaction coefficient term on the nonlinear boundary condition, we obtain different regimes establishing effective homogenized limits in N-dimensional open bounded sets. In order to do that, we combine monotone operator analysis techniques and the unfolding method used to deal with asymptotic analysis and homogenization problems. (AU)

• FAPESP's process: 22/08112-1 - Boundary perturbation problems on partial differential equations
• Grantee: Jean Carlos Nakasato
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 20/14075-6 - Dynamical systems and their attractors under perturbations
• Grantee: Alexandre Nolasco de Carvalho
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 20/04813-0 - Asymptotic and qualitative analysis of integro-differential equations
• Grantee: Marcone Corrêa Pereira
• Support Opportunities: Regular Research Grants