2022/05/19 by D. I. Borisov, Borisov, Denis I. · 2 citations
Computer Science · Engineering · Mathematics · #35B27 #35B40 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2205.09490
openalex publication_date 2022/05/19 · openalex created_date 2022/05/23 · openalex updated_date 2026/07/28
We consider a boundary value problem for a general second order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries of the cavities are subject either to a Dirichlet or a nonlinear Robin condition. On the perforation, certain rather weak conditions are imposed to ensure that under the homogenization we obtain a similar problem in a non-perforated domain with an additional potential in the equation usually called a strange term. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in W21- and L2-norms uniformly in L2-norm of the right hand side in the equation. The estimates for the convergence rates are established and their order sharpness is discussed.