Abstract. We use the variational concept of Γ -convergence to obtain sufficient conditions that guarantee existence, stability and the geometric structure of four families of stationary solutions to the singularly perturbed parabolic equation ∂ t u ε = ε 2 Δu ε + f (u ε ,x) on surfaces of revolution. We consider the bistable function f (u, (u − c(x)) and the conditions found relate the functions a,b,c to the geometry of the surface where such functions are defined.Mathematics subject classification (2010): 35K57, 35B36, 35R01, 35B25, 35B35, 34K20, 58J32.
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