Nonlinear diffusion equations as asymptotic limits of Cahn‐Hilliard systems on unbounded domains via Cauchy's criterion

@article{Fukao2017NonlinearDE,
  title={Nonlinear diffusion equations as asymptotic limits of Cahn‐Hilliard systems on unbounded domains via Cauchy's criterion},
  author={Takeshi Fukao and Shunsuke Kurima and Tomomi Yokota},
  journal={Mathematical Methods in the Applied Sciences},
  year={2017},
  volume={41},
  pages={2590 - 2601}
}
This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial‐boundary problem for the nonlinear diffusion equation in an unbounded domain Ω⊂RN ( N∈N ), written as ∂u∂t+(−Δ+1)β(u)=ginΩ×(0,T), which represents the porous media, the fast diffusion equations, etc, where β is a single‐valued maximal monotone function on R , and T>0. In Kurima and Yokota (J Differential Equations 2017; 263:2024‐2050 and Adv Math Sci Appl 2017; 26… 
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Asymptotic analysis for Cahn–Hilliard type phase‐field systems related to tumor growth in general domains
  • Shunsuke Kurima
  • Mathematics
    Mathematical Methods in the Applied Sciences
  • 2019
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Time discretization of a nonlinear phase field system in general domains
TLDR
It turns out that the nonlinear phase field system is a generalization of the Caginalp phase field model and it has been studied by many authors in the case that £Omega $\end{document} is a bounded domain, but for unbounded domains the analysis of the system seems to be at an early stage.

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