Global Existence for Nonlocal Quasilinear Diffusion Systems in Non-Isotropic Non-Divergence Form
arxiv(2022)
摘要
Consider the quasilinear diffusion problem
𝐮'+Π(t,x,𝐮,Σ𝐮)𝔸𝐮=𝐟(t,x,𝐮,Σ𝐮) in ]0,T[×Ω,
𝐮=0 in
]0,T[×Ω^c,
𝐮(0,·)=𝐮_0(·) in
Ω
for an open set Ω⊂ℝ^n,
𝐮_0∈𝐇^s_0(Ω):=[H^s_0(Ω)]^m and any
T∈]0,∞[, where Σ𝐮∈ℝ^q for 0
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