摘要：In this paper, we study the parabolic Monge–Ampère equations $-u_{t}\det (D^{2}u)=g$ outside a bowl-shaped domain with g being the perturbation of $g_{0}( x )$ at infinity. Under the weaker conditions compared with the problem outside a cylinder, we obtain the existence and uniqueness of viscosity solutions with asymptotic behavior for the first initial-boundary value problem by using the Perron method.
关键词：Parabolic Monge–Ampère equations ; Initial-boundary value problem ; Bowl-shaped domain ; Perron method ; Asymptotic behavior
