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math.AP2007★ 1 cited
Relaxation of the flow of triods by Curve Shortening Flow via the vector-valued parabolic Allen-Cahn equation
Mariel Saez Trumper
In this paper we find solutions to a certain class of vector-valued parabolic Allen-Cahn equation that as develops as interface a given triod evolving under curve sh…
math.AP2007★ 2 cited
Existence of a solution to a vector-valued Allen-Cahn equation with a three well potential
Mariel Saez Trumper
In this paper we prove existence of a vector-valued solution to -Δv +\frac{\nabla_v W(v)}{2}&=0, \lim_{r\to \infty}v(r \cosθ,r\sinθ)&= c_i \hbox{for} θ\in (θ_{i-1}, θ_i), where…