TY - JOUR AU - Dai, Limei AU - Cheng, Huihui PY - 2021 DA - 2021/03/10 TI - The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain JO - Boundary Value Problems SP - 29 VL - 2021 IS - 1 AB - 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. SN - 1687-2770 UR - https://doi.org/10.1186/s13661-021-01505-w DO - 10.1186/s13661-021-01505-w ID - Dai2021 ER -