The brain itself will not continue to 'think' as it will be dead!! However, depending on your belief system in the hereafter, you can choose to believe that death is final in terms of mortality, or you can believe otherwise. I believe that what makes us 'us' is more than physical and that we have a soul, which carries on after our physical bodies are dead. I could liken it to electricity; you can't see it but if you stuck your finger in the socket, you'd soon know it was there!! I could carry on for many paragraphs about this but I'll leave it at that!