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Homogenization of quasilinear parabolic problems with alternating nonlinear Fourier and uniform Dirichlet boundary conditions in a thick two-level junction of type \(3:2:2\). (Ukrainian. English summary) Zbl 1289.35025
The authors study asymptotic properties of solutions to quasilinear parabolic problems in a thick two-level junction of type \(3:2:2.\) The junction consists of a cylinder \(\Omega_0\) with \(\varepsilon\)-periodically strung thin disks of variable thickness. In addition, the disks are divided into two levels depending on their geometric structure and boundary conditions. The problems are considered with alternating uniform Dirichlet and nonlinear Fourier conditions. The last boundary conditions depend on additional perturbed parameters. Depending of the additional parameters theorems on convergence (as \(\varepsilon \to 0)\) are proved and influence of the boundary conditions on the asymptotic properties of the solutions is studied.
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
74K30 Junctions