My 3000 GT turns 0ff while driving

I have a 1991 Mitsubishi 3000 GT that has trouble staying on. It will turn off while driving or even when its just sitting in the parking lot. Sometimes i can start it right away or sometimes i have to wait a while. When I start my car it runs rich at first , like at 1500 rpm. then after I drive it for a while it drops to about 500 rpm.