need help with date compare

I'm trying to retrieve an expiration date from a database and compare it to today's date. If the expiration date hasn't arrived yet, I want to redirect the program, if if it has I want to display a message.

<?php

mysql_connect(localhost,root,"");

mysql_select_db(expiredb) or die( "Unable to select database");

if(!empty($_POST["submit"]))

{

$noticedate = $_POST['noticedate'];

$expiredate = $_POST['expiredate'];

$query="SELECT noticedate,expiredate FROM entrydata";

$result=mysql_query($query);

if(mysql_num_rows($result))

{

$todays_date = date("Y-m-d");

$today = strtotime($todays_date);

$expiration_date = strtotime($expiredate);

if ($expiration_date > $today) {



header("Location: hammockoaks.html");

exit;    

}

elseif ($expiration_date =  $today) {

header("Location: hologo.html");

}else {

}

}// end of it statement for 'results found'

echo '_POST["submit"] is actually empty.';

}// end of if statement for no 'submit'

 ?>