Not so much a malfunction as the fact that power failed (both external and their backup generators). The problem is that "shutting down" a reactor is not an easy process. Stopping the chain reaction can be done very quickly, and as far as I heard was done successfully in all reactors. However, a lot of the most highly radioactive fission products emit so much radiation that they create insane amounts of heat for days or weeks and require constant cooling. So when the power went down, the cooling system failed, reactor cores heated up, meltdown, etc. There are other risks involved in this as well (extreme heat can initiate reactions that produce highly explosive hydrogen case from the water in the reactor, for example). That's also why even the three reactor cores that hadn't even been running before the Earthquake were having trouble, and why one of them even suffered an explosion.