Fetch the input type date value via ajax

If you want to post the value as soon as user has entered the date and click somewhere else, this might help you:

 jQuery('#your-name').on('blur', function(){
   var date_Value = this.value;
   var ajaxdata = {
        action: 'process_date',
        date_value: date_Value
    };
   jQuery.post(ajaxurl, ajaxdata, function(res){ 
      /* whatever you want to do, res contains the output generated by your php file*/  
    });
 })

As you are using admin ajax, make a function to process this data.

function process_Date(){
  $date = $_POST['date_value'];
  /* do whatever you want to do with your $date*/
 /* return an output */
  die(1);
}
add_action('wp_ajax_process_date', 'process_Date');
add_action('wp_ajax_nopriv_process_date', 'process_Date');

Add this function to your file where you are having other functions.