Existence of Solutions to a Cahn-Hilliard Type Equation with a Logarithmic Nonlinear Term

被引：10
|
作者：
Miranville, Alain [1 ,2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen, Fujian, Peoples R China
[2] Univ Poitiers, CNRS, Equipe DACTIM MIS, Lab Math & Applicat,UMR 7348, Blvd Marie & Pierre Curie Teleport 2, F-86962 Futuroscope, France
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2019年 / 16卷 / 01期
关键词：
Cahn-Hilliard equation; proliferation term; logarithmic nonlinear term; existence; blow up; 35K55; 35B45; ASYMPTOTIC-BEHAVIOR; DISCONTINUOUS GALERKIN; PHASE-SEPARATION; BINARY-MIXTURES; MODEL; ATTRACTORS; EVOLUTION; GROWTH; SYSTEM;
D O I：
10.1007/s00009-018-1284-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Our aim in this paper is to prove the existence of solutions to a Cahn-Hilliard type equation with a proliferation term and a logarithmic nonlinear term. Such an equation was proposed in view of biological applications. The main difficulty comes from the fact that we no longer have the conservation of the spatial average of the order parameter, contrary to the original Cahn-Hilliard equation. This makes the derivation of uniform (with respect to the regularization parameter) estimates on the solutions to approximated problems delicate, as blow up in finite time may occur.
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收藏
页数：18
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