mWebView.setDownloadListener(new DownloadListener() {
    public void onDownloadStart(String url, String userAgent,
            String contentDisposition, String mimetype,
            long contentLength) {
                Request request = new Request( Uri.parse(url));
                request.allowScanningByMediaScanner();
                request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);
                request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, "myPDFfile.pdf"); 
                DownloadManager dm = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
                dm.enqueue(request);        
   }
});