# 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}
}
• Published 27 November 2015
• Mathematics
• Mathematical Methods in the Applied Sciences
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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