Charlie S. asks:

Either install a door closing mechanism, so that the door will close
by itself or maybe add a magnet to the frame and a piece of iron to
the door so that it's kept closed.

Closing mechanism. as like those found on a swinging screen door ? Or, are
you referring to something else?

A pneumatic closer, I'd guess. They are easy to install, not super expensive,
and will solve your problem. You'll see counterparts on many commercial doors,
restrooms, etc. You'd probably need one of the ligest duty models available.

Screen door springs *might* work if your door weighs about what a screen door
does.

Charlie Self
"One of the common denominators I have found is that expectations rise above
that which is expected." George W. Bush