I would highly recommend that you separate your user input pages from your input processing pages. I usually just add a "_p" suffix to the page name (i.e. - the processing page for edit_user.php would be edit_user_p.php). There are several benefits to this development style:
1) Bandwidth and processing is saved when users don't follow through on an action
2) Re-posting of user input is rarely a concern and page navigation is simpler
3) It breaks up code into smaller chunks that are easy to work with
4) It makes pages easier to "template" and reuse
I would assume that there are two pages in your example code:
1) the user input page that you listed
2) the search page, which probably combines processing and results (which is appropriate for a search function)
The search page will take the input from the page you listed, perform the search based on the input, and display the results of the search.
Note: You'll find that many developers will combine the input, search, and results into the same page, which I tend to discourage. It makes code more complicated than it needs to be, wastes bandwidth (if the user doesn't actually go through with the search, why load and process all of that code???), and it makes troubleshooting more difficult.