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.

中文翻译：

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描述受损心脏组织中生物电活动的改良双域模型的良好状态

我们证明了修改后的双域模型的解决方案的存在和唯一性，描述了病理情况下心脏组织的电行为。主要思想是将问题简化为抽象的抛物线设置，这需要引入几个辅助微分系统和一个非标准的双线性形式。主要困难是由于双域系统的简并性及其与扩散方程的非标准耦合，说明了心脏组织中病理区的存在。