Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue

被引：65
|
作者：
Bendahmane, Mostafa [1 ]
Karlsen, Kenneth H. [1 ]
机构：
[1] Univ Oslo, Ctr Math Applicat, N-0316 Oslo, Norway
来源：
NETWORKS AND HETEROGENEOUS MEDIA | 2006年 / 1卷 / 01期
关键词：
reaction-diffusion system; degenerate; weak solution; existence; uniqueness; bidomain model; cardiac electric field;
D O I：
10.3934/nhm.2006.1.185
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove well-posedness (existence and uniqueness) results for a class of degenerate reaction-diffusion systems. A prototype system belonging to this class is provided by the bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The existence result, which constitutes the main thrust of this paper, is proved by means of a nondegenerate approximation system, the Faedo-Galerkin method, and the compactness method.
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页码：185 / 218
页数：34
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