Strong time-periodic solutions to the bidomain equations with arbitrary large forces. (June 2019)

• Record Type: Journal Article
• Authors: Giga, Yoshikazu; Kajiwara, Naoto; Kress, Klaus
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 398
• Page End: 413
• Publication Date: 2019-06
• Subjects: Bidomain model -- Strong periodic solutions -- Weak–strong uniqueness -- Large data; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.11.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We prove the existence of strong time-periodic solutions to the bidomain equations with arbitrary large forces. We construct weak time-periodic solutions by a Galerkin method combined with Brouwer's fixed point theorem and a priori estimate independent of approximation. We then show their regularity so that our solution is a strong time-periodic solution in L 2 spaces. Our strategy is based on the weak–strong uniqueness method.