Patterns with prescribed numbers of critical points on topological tori

Abstract

We study the existence of critical points of stable stationary solutions to reaction–diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with prescribed numbers of critical points whose locations are explicit.

Keywords:

• Stable solution
• pattern
• semilinear elliptic equation
• reaction–diffusion equation
• standard torus
• critical point

AMS Subject Classifications:

• Primary: 35B35
• Secondary: 35K57
• 35K58
• 35J61
• 35P15
• 35K15
• 35K20
• 35B20
• 58J05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Grant-in-Aid for Scientific Research (B) of Japan Society for the Promotion of Science 18H01126