Stationary waves on the sphere

Slawomir Bialecki, Bogdan Kazmierczak, Je-Chiang Tsai

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we investigate stationary waves on the sphere using the bistable reaction-diffusion system. The motivation of this study arises from the study of activation waves of B cells in immune systems. We analytically establish (i) the existence and uniqueness of stationary waves; (ii) the limiting wave profile for small diffusivity of diffusing species; and (iii) the stability of the constructed stationary waves. The stability result may suggest the critical role of stationary waves in the determination of initial data for initiating propagating waves on the sphere, which is consistent with the numerical results for the B-cell activation model.

Original languageEnglish
Pages (from-to)1761-1788
Number of pages28
JournalSIAM Journal on Applied Mathematics
Volume75
Issue number4
DOIs
Publication statusPublished - 2015 Jan 1

Fingerprint

B Cells
Activation
Chemical activation
Cells
Bistable System
Immune system
Immune System
Diffusivity
Reaction-diffusion System
Existence and Uniqueness
Limiting
Numerical Results
Model
Profile

Keywords

  • Bistable kinetics
  • Sphere
  • Stationary wave

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Stationary waves on the sphere. / Bialecki, Slawomir; Kazmierczak, Bogdan; Tsai, Je-Chiang.

In: SIAM Journal on Applied Mathematics, Vol. 75, No. 4, 01.01.2015, p. 1761-1788.

Research output: Contribution to journalArticle

Bialecki, Slawomir ; Kazmierczak, Bogdan ; Tsai, Je-Chiang. / Stationary waves on the sphere. In: SIAM Journal on Applied Mathematics. 2015 ; Vol. 75, No. 4. pp. 1761-1788.
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