On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data | Zendy

Matthieu Alfaro | Zendy; Hiroshi Matano | Zendy

Open Access

On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data

Author(s) -

Matthieu Alfaro,

Hiroshi Matano

Publication year - 2012

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2012.17.1639

Subject(s) - allen–cahn equation , class (philosophy) , mathematics , term (time) , type (biology) , diffusion , calculus (dental) , mathematical analysis , computer science , physics , medicine , thermodynamics , ecology , dentistry , biology , quantum mechanics , artificial intelligence

Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Nagumo system. Despite their successful role, it has been largely unclear whether or not such expansions really represent the actual profile of solutions with rather general initial data. By combining our earlier result and known properties of eternal solutions of the Allen-Cahn equation, we prove validity of the principal term of the formal expansions for a large class of solutions.

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