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Numerically solving a system of PDEs where one function is composed with the other

I'm trying to solve the following system using NDSolve: $$ \begin{align} u_t(x,t) &= u_{xx}(x,t) - v(x,t) \\ v_t(x,t) &= u(v(x,t),t) \end{align} $$ with $$ u_x(-1,t) = 0, \quad u_x(1,t) = 0, \quad …
Antonio Vargas's user avatar