一个描述受损心脏组织生物电活动的修正bidomain模型的适定性
Well-posedness for a modified bidomain model describing bioelectric activity in damaged heart tissues
摘要：
我们证明了一个修改后的bidomain模型的解决方案的存在性和唯一性，描述的病理情况下的心脏组织的电行为。其主要思想是将问题归结为一个抽象的抛物型问题，这需要引入几个辅助微分系统和一个非标准的双线性型。主要的困难是由于bidomain系统的简并性及其与扩散方程的非标准耦合，从而解释了心脏组织中病理区的存在。
英文摘要：
We prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The leading idea is to reduce the problem to an abstract parabolic setting, which requires to introduce several auxiliary differential systems and a non-standard bilinear form. The main difficulties are due to the degeneracy of the bidomain system and to its non-standard coupling with a diffusion equation, accounting for the presence of the pathological zone in the heart tissue.
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