2022/05/30 by Pardeep Kumar, Kumar, Pardeep, Manil T. Mohan +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2205.14866
openalex publication_date 2022/05/30 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \boldsymbolut-μΔ\boldsymbolu+(\boldsymbolu⋅∇)\boldsymbolu+α\boldsymbolu+β|\boldsymbolu|r-1\boldsymbolu+∇ p=\boldsymbolF:=f \boldsymbolg, ∇⋅\boldsymbolu=0, in a bounded domain Ω⊂ℝ2 with smooth boundary ∂Ω, where α,β,μ>0 and r∈[1,3]. The investigated inverse problem consists of reconstructing the vector-valued velocity function \boldsymbolu, the pressure field p and the scalar function f. For the divergence free initial data \boldsymbolu0 ∈ \mathbbL2(Ω), we prove the existence of a solution to the inverse problem for two-dimensional CBF equations with the integral overdetermination condition, by showing the existence of a unique fixed point for an equivalent operator equation (using an extension of the contraction mapping theorem). Moreover, we establish the uniqueness and Lipschitz stability results of the solution to the inverse problem for 2D CBF equations with r ∈[1,3].