Existence of radially symmetric patterns for a diffusion problem with variable diffusivity

Abstract

We give a sufficient condition for the existence of radially symmetric stable stationary solution of the problem $u_t=\operatorname{div}(a^2\nabla u)+f(u)$ on the unit ball whose border is supplied with zero Neumann boundary condition. Such a condition involves the diffusivity function $a$ and the technique used here is inspired by the work of E. Yanagida.

Keywords

• diffusion problem
• stable solutions
• radially symmetric solution
• variable diffusivity
• patterns