On a resolvent estimate for bidomain operators and its applications. (English) Zbl 1380.35033
Summary: We study bidomain equations that are commonly used as a model to represent the electrophysiological wave propagation in the heart. We prove existence, uniqueness and regularity of a strong solution in \(L^p\) spaces. For this purpose we derive an \(L^\infty\) resolvent estimate for the bidomain operator by using a contradiction argument based on a blow-up argument. Interpolating with the standard \(L^2\)-theory, we conclude that bidomain operators generate \(C_0\)-analytic semigroups in \(L^p\) spaces, which leads to construct a strong solution to a bidomain equation in \(L^p\) spaces.
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
bidomain model; blow-up argument; PDE-ODE system; electrophysiological wave propagation in the heart; contradiction argument; analytic semigroupsReferences:
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