Homogenization of locally periodic parabolic operators with non-self-similar scales

2021/03/02 by Jun Geng, Geng, Jun, Weisheng Niu +1
Computer Science · Engineering · Mathematics · #35B27 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2103.01418

openalex publication_date 2021/03/02 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28

Abstract

We investigate quantitative estimates in homogenization of the locally periodic parabolic operator with multiscales ∂_t- div (A(x,t,x/ε,t/κ²) ∇ ), \varepsilongt;0, κgt;0. Under proper assumptions, we establish the full-scale interior and boundary Lipschitz estimates. These results are new even for the case κ=ε, and for the periodic operators ∂_t-div(A(x/ε, t/ε^ℓ) ∇ ), 0

Citations

• Quantitative Estimates in Homogenization of Parabolic Systems of Elasticity in Lipschitz Cylinders

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