Read through the OP, this coin has a great concept!
what happens after 5 weeks. All miners will leave, no one is going fight for 1 mint. How is this supposed to work?
Google for Proof-of-Stake Algorithm. After 5 weeks new coins are generated as a form of interest, no need for miners. The network will be secured even without miners. When holding a certain amount of coins for a certain amount of time in your wallet, new blocks will be generated automatically from it.
the question is who will process SEND transactions.
I suppose it works similar like with Nextcoin, which is explained here:
http://bitcoin.stackexchange.com/questions/20007/how-does-proof-of-stake-mining-workIn Nextcoin, proof of stake is used. So the "mining" process there is just about holding coins and leaving your computer on. It doesn't involve powerful CPUs.
Each block (every 60 seconds), a random Nextcoin is selected to be the next "miner". There are 1 billion coins so the odds of a single wallet being selected is the number of Nxt in that wallet divided by 1 billion. (Also, it's possible to calculate and agree on who that node is so the transactions need only be sent to that particular wallet.)
If a node with the selected wallet is running, it will collect the transactions, make a block, and send it to the rest of the network and collect the fees. If the computer is turned off, however, then the entire network will have to select a different nextcoin to make the transaction. This time, the unresponsive wallet will be ignored. The network would suffer in that the time to make a block is decreased, but the thought is that people wouldn't leave their computers off if they have a lot of NXT because they're missing out on all the fees that they could have collected.