Problem with Sessions Authentication in Html5 members-site pages (PhoneGap)

Here's a Problem with Sessions Authentication in Html5 members-site pages. We use PhoneGap to convert the Html5 pages into mobile app. But unfortunately, this Html5 cannot do processing of data in Php. Therefore, in creating a members-On creating a members login-site with PhoneGap, understand we use Ajax to interchange data between Html5 and Php. Analogous to the Isset (Session) in Php, could sessions on Html5 be checked for being same as that on the Php, to authenticate members to login? Because Isset (Sessions) is used in php to check if a member is already logged in earlier, and remains logged in. So, if it is true, member is granted access to internal pages on the site. But on Html5 site pages on the PhoneGap application, the data interchange with Php is done through Ajax. That means the sessions is stored in Html5 and not on the Php server. Would this present a contradiction or dilemma, as the sessions on Html5 pages and that on the Php server are on separate places. As I do not want to use Parse or Heroku to do this, somehow, it must be possible to build the Phone Gap's Html 5 with successful processing of data from Php going to and coming back from. Propose me your ideas and workable solutions will be delegate to the preferred programmer.