2000 Maxima Shuts off in Idle

I have 2000 maxima for over 3 years already and have no major problems. However, I recently noticed that when I start the car it starts just fine, but if i drive it for a few minutes to the nearest grocery store, then put it in park, it idle's for 2-3 minutes, then shuts itself off. What could possibly be the problem? In addition, I've noticed a slip when it changes gears from the automatic transmission. When i drive the car cold it does not slip and picks up as though the car were brand new again. Could there be a possibility that debris is causing it to slip? I'm in desperate need of some advice here because this problem has become very annoying lately.

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Super_Dave
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