[Hoshinokoe]

alex2012,

<textarea id="text"></textarea>
<input name="button" type="submit" value="Отправить" id="sendwellmini">

<script type="text/javascript">
$('input[name="button"]').on("click",function(){
   var val = $("#text").val();
   alert(val);
});
</script>

P.S. опечатка.