On the bidomain problem with FitzHugh–Nagumo transport

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The bidomain problem with FitzHugh–Nagumo transport is studied in the (Formula presented.)-framework. Reformulating the problem as a semilinear evolution equation, local well-posedness is proved in strong as well as in weak settings. We obtain solvability for initial data in the critical spaces of the problem. For dimension (Formula presented.), by means of energy estimates and a recent result of Serrin type, global existence is shown. Finally, stability of spatially constant equilibria is investigated, to the result that the stability properties of such equilibria are the same as for the classical FitzHugh–Nagumo system in ODE’s. These properties of the bidomain equations are obtained combining recent results on the bidomain operator (Hieber and Prüss in Theory for the bidomain operator, submitted, 2018), on critical spaces for parabolic evolution equations (Prüss et al in J Differ Equ 264:2028–2074, 2018), and qualitative theory of evolution equations.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalArchiv der Mathematik
DOIs
Publication statusAccepted/In press - 2018 Jun 14
Externally publishedYes

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Evolution Equation
Semilinear Evolution Equation
Local Well-posedness
Energy Estimates
Operator
Global Existence
Parabolic Equation
Solvability
Framework

Keywords

  • Bidomain operator
  • Critical spaces
  • FitzHugh–Nagumo transport
  • Global existence
  • Maximal $$L_p$$Lp-regularity
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the bidomain problem with FitzHugh–Nagumo transport. / Hieber, Matthias Georg; Prüss, Jan.

In: Archiv der Mathematik, 14.06.2018, p. 1-15.

Research output: Contribution to journalArticle

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