A note on existence of patterns on surfaces of revolution with nonlinear flux on the boundary

Abstract

In this note we address the question of existence of non-constant stable stationary solution to the heat equation on surfaces of revolution subject to nonlinear boundary flux involving a positive parameter. Our result is independent of the surface geometry and, in addition, we provide the asymptotic profile of the solutions and some examples where the result applies.

Keywords

• patterns
• surface of revolution
• nonlinear flux
• sub-supersolution method
• linearized stability