Well-posedness for a modified bidomain model describing bioelectric activity in damaged heart tissues
| Autor: | Micol Amar, Claudia Timofte, Daniele Andreucci |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
abstract parabolic equations
Diffusion equation 35K90 35A01 35K20 35Q92 General Mathematics Quantitative Biology::Tissues and Organs existence uniqueness bidomain model imperfect transmission conditions Physics::Medical Physics Bidomain model Bilinear form Coupling (electronics) Mathematics - Analysis of PDEs Heart tissues FOS: Mathematics Applied mathematics Uniqueness Degeneracy (mathematics) Well posedness Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2101.09285 |
| Popis: | 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. Comment: 19 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2101.09112 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|