Interface dynamics for an Allen-Cahn-type equation governing a matrix-valued field

Dong Wang, Braxton Osting, Xiao-Ping Wang

We consider the initial value problem for the generalized Allen-Cahn equation, \[\partial_t Φ= ΔΦ-\varepsilon^{-2} Φ(Φ^t Φ- I), \qquad x \in Ω, \ t\geq 0,\] where $\Phi$ is an $n\time…