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We study bidomain equations that are commonly used as a model to representthe electrophysiological wave propagation in the heart. We prove existence,uniqueness and regularity of a strong solution in $L^p$ spaces. For thispurpose we derive an $L^\infty$ resolvent estimate for the bidomain operator byusing a contradiction argument based on a blow-up argument. Interpolating withthe standard $L^2$-theory, we conclude that bidomain operators generate$C_0$-analytic semigroups in $L^p$ spaces, which leads to construct a strongsolution to a bidomain equation in $L^p$ spaces.

On a resolvent estimate for bidomain operators and its applications