Кнопка "Отправить" не работает в форме "Bootstrap"

У меня есть форма в Bootstrap 3, которая внутри модального. Там кнопка, называемая "отправить", когда при нажатии на материал, который был введен в форму, должен быть отправлен на адрес электронной почты. Хотя, когда я нажимаю "Отправить", ничего не происходит.

Кто-нибудь знает, почему это происходит? Здесь форма:

<div class="modal fade" id="contactPop" tabindex="-1" role="dialog" aria-labelledby="contactModal" aria-hidden="true">
     <div class="modal-dialog">
        <div class="modal-content">
           <div class="modal-header">
              <!-- Close button. -->
              <button type="button" class="close" data-dismiss="modal" aria-hidden="true">&times;</button>
              <!-- Title. -->
              <h3 class="modal-title" style="font-family: 'Lato', sans-serif; font-weight: 700;">
                 Contact Us <small style="font-family: 'Lato', sans-serif; font-weight:400;"> You matter to us.</small>
              </h3>
           </div>

           <!-- User input fields. -->
           <form class="contact" action="process.php" method="post">
           <div class="modal-body">
              <div class="row">
                 <div class="col-sm-6">
                    <label class="control-label">Subject</label>
                    <input type="text" class="form-control" required="required" placeholder="I aciddentally the website!" name="subject">
                 </div>
                 <div class="col-sm-6">
                    <label class="control-label">Username</label>
                    <input type="text" class="form-control" required="required" placeholder="Notch" name="username">
                 </div>
              </div>
              <br>

              <div class="row">
                 <div class="col-sm-6">
                    <label class="control-label">Message</label>
                    <textarea class="form-control" rows="8" style="resize: vertical;" required="required" placeholder="Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam eget fermentum justo, sit amet semper." name="message"></textarea>
                 </div>

                 <div class="col-sm-6">
                    <label class="control-label">Email</label>
                    <input type="email" class="form-control" required="required" placeholder="[email protected]" name="email">
                 </div>

                 <div class="col-sm-6" style="line-height: 21px;">
                    <br>
                    <p>Responses are usually received within 1-2 business days.</p>
                    <p>Please be as clear and concise as possible, in order to help us process your inquiry faster.</p>
                 </div>
              </div>
           </div>

           <!-- Close & submit buttons. -->
           <div class="modal-footer">
              <button type="button" class="btn btn-info" data-dismiss="modal"><i class="glyphicon glyphicon-remove"></i> Close</button>
              <button type="button" value=" Send" class="btn btn-success" type="submit" id="submit"><i class="glyphicon glyphicon-inbox"></i> Submit</button>
           </div>
        </div>
     </div>
  </div>

Там также process.php, который отправляет форму, которая находится здесь:

<?php
//add the recipient address here
$myemail = '[email protected]';

//grab named inputs from html then post to #thanks
if (isset($_POST['name'])) {
$name = strip_tags($_POST['name']);
$email = strip_tags($_POST['email']);
$message = strip_tags($_POST['message']);
echo "<span class=\"alert alert-success\" >Your message has been received, and we will get                 back to you as soon as possible. Here is what you submitted:</span><br><br>";
echo "<stong>Name:</strong> ".$name."<br>";   
echo "<stong>Email:</strong> ".$email."<br>"; 
echo "<stong>Message:</strong> ".$message."<br>";

//generate email and send!
$to = $myemail;
$email_subject = "Contact form submission: $name";
$email_body = "You have received a new message. ".
" Here are the details:\n Name: $name \n ".
"Email: $email\n Message \n $message";
$headers = "From: $myemail\n";
$headers .= "Reply-To: $email";
mail($to,$email_subject,$email_body,$headers);
}
?>

А затем в индексе есть также javascript, который должен отправить форму.

 <script type="text/javascript">
     $(document).ready(function () {
$("input#submit").click(function(){
    $.ajax({
        type: "POST",
        url: "process.php", //process to mail
        data: $('form.contact').serialize(),
        success: function(msg){
            $("#thanks").html(msg) //hide button and show thank you
            $("#form-content").modal('hide'); //hide popup  
        },
        error: function(){
            alert("failure");
        }
    });
});
});
  </script>

Если кто-то может помочь, это будет очень полезно!