A Free Boundary Problem With Two Different Free Boundaries

i~jE A free boundary problem with two different kinds &f free boundaries Abstract In this paper we will study the existence and uniqueness of the local(time) solution of a free boundary problem arising from industry with two free boundaries. In order to obtain the existence we will first study the problem with one free boundary fixed (We call this problem (1)). I prove the existence and uniqueness of this problem by the same method in [1]. This proof depends cm a boundary point principal of infinite zonal area. Then fix another free boundary of the origin problem and obtain problem (2) ,this problem has been worked out by [4].By these two results ,we prove the existence of the origin problem by fixed point principal. We will prove a pare of estimates to obtain the uniqueness of the problem .Each of these two estimates comes from the continuality of the free boundary to the vibrate of the fixed boundary in (1) or (2).The right const of the estimates coming from (2) is CT. So, we can obtain the uniqueness of the origin problems. Zhao Guang(Applied Mathematics) Directed by Prof.FaHuai Yi...