Turing patterns for a coupled two-cell generalized Schnakenberg model

ABSTRACT

We consider a system for a generalized Schnakenberg model, showing Turing pattern formation for a wide class of nonlinearities.

COMMUNICATED BY:

• D. Repov

KEYWORDS:

• Schnakenberg model
• two-cell
• pattern formation
• a priori estimate
• steady state

AMS SUBJECT CLASSIFICATIONS:

• 35J57
• 47H11
• 92C15
• 35B45
• 35B36
• 35A01

Acknowledgments

The authors are grateful to the anonymous referees for their suggestions, which improved the presentation of the paper, and for bringing [18,19] and [20] to their attention.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Genni Fragnelli http://orcid.org/0000-0002-5436-7006

Dimitri Mugnai http://orcid.org/0000-0001-8908-5220

Additional information

Funding

Genni Fragnelli was partially supported by the FFABR ‘Fondo per il finanziamento delle attività base di ricerca’ 2017, by ‘Fondi di Ricerca di Ateneo’ 2015–2016 ‘Problemi differenziali nonlineari’, by the GNAMPA project 2019 ‘Controllabilità di PDE in modelli fisici e in scienze della vita’ and by the Italian MIUR (Ministero dell'Istruzione, dell'Università e della Ricerca) national project Qualitative and quantitative aspects of PDEs (2017JPCAPN). Dimitri Mugnai was partially supported by the Italian MIUR (c) national project Variational methods, with applications to problems in mathematical physics and geometry (2015KB9WPT_009) and by the FFABR Fondo per il finanziamento delle attività base di ricerca 2017. Both authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).