Non-dissipative system as limit of a dissipative one: comparison of the asymptotic regimes

2018/10/06 by da Silva, Silva, Ricardo P.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.03054

openalex publication_date 2018/10/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℝⁿ be a bounded smooth domain (open and connected) in ℝⁿ. Given u₀∈ L²(Ω), g∈ L^∞(Ω) and λ∈ ℝ, our purpose is to describe the asymptotic behavior of weak solutions of the family of problems \ \dfrac∂ u∂ t - Δ_p u · amp; = · amp; λu + g, · amp; on (0,∞)× Ω,
u · amp; = · amp; 0, · amp; in (0,∞)× ∂ Ω,
u(0, ⋅) · amp; = · amp; u₀, · amp; on Ω, . as p \longrightarrow 2⁺, where Δ_p u:=\rmdiv(|∇ u|^p-2∇ u) denotes the p-laplacian operator.

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