Electron. J. Diff. Equ., Vol. 2014 (2014), No. 238, pp. 1-13.

Patterns on surfaces of revolution in a diffusion problem with variable diffusivity

Arnaldo Simal do Nascimento, Maicon Sonego

In this article we study the existence of non-constant stable stationary solutions to the the diffusion equation $u_t=\hbox{div}(a \nabla u)+f(u)$ on a surface of revolution whose border is supplied with zero Neumann boundary condition. Sufficient conditions on the geometry of the surface and on the diffusivity function a are given for the existence of a function f such the problem possesses such solutions.

Submitted January 16, 2014. Published November 13, 2014.
Math Subject Classifications: 35K57, 35B36, 35R01, 35B25, 35B35, 34K20, 58J32.
Key Words: Patterns; diffusion; surface of revolution; stability.

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Arnaldo S. do Nascimento
Universidade Federal de São Carlos - D. M.
S. Carlos, S. P., Brasil
email: arnaldon@dm.ufscar.br
Maicon Sônego
Universidade Federal de Itajubá - IMC
Itajubá, M. G. Brasil
email: mcn.sonego@unifei.edu.br

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