2020/03/27 by Sung‐Hoon Kim, Kim, Sunghoon, Ki-Ahm Lee +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2003.12241
openalex publication_date 2020/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the solution \boldu=(u1,⋯,uk) of the generalized parabolic system (ui)t=∇⋅(mUm-1A(∇ ui,ui,x,t)+B(ui,x,t)), (1≤ i≤ k) in the range of exponents m>(n-2)/(n) where the diffusion coefficient U depends on the components of the solution \boldu. Under suitable structure conditions on the vector fields A and B, we first show the uniform L∞ bound of the function U for t≥ τ>0 and law of L1 mass conservation of each component ui, (i=1,⋯,k), with system version of Harnack type inequality. As the last result, we also deal with the local continuity of solution \boldu=(u1,⋯,uk) with the intrinsic scaling. If the ratio between U and components ui, (i=1,⋯,k), is uniformly bounded above and below, all components of the solution \boldu have the same modulus of continuity.