关键词: 抛物型Monge-Ampère方程, 初边值问题, 最优投资问题

Abstract:

This paper deals with the first initialboundary value
 problem of a onedimension parabolic Monge-Ampère equation come from the the
ory of optimal investment. The existence of the classical solution was establish
ed by means of the combination of the method of continuity with a priori estimat
ion of the problem. The uniqueness of the solution is a direct conclusion from t
he maximum principle. The result of paper can be regarded as an extendence of a
result of the correlative problem of parabolic MongeAmpère equation  -u_tdet(u_ij)=f(x,t)  in one dimension.

Key words: parabolic MongeAmpère equation, initialboundary value problem, optimal investment