Exterior problems for a parabolic Monge–Ampère equation

In this paper, we study the exterior problem for a parabolic Monge–Ampère equation ut−logdet(D2u)=f(x,t)ut−logdet(D2u)=f(x,t). The existence and uniqueness of the viscosity solution with asymptotic behavior at infinity are established by the Perron method. We generalize the results of exterior problems for the elliptic Monge–Ampère equation.