integrated Windows authentication

Hi guy's,
I am a newbie with Tomcat and maybe someone can answer this question.
We have DomainA and DomainB and there is a 2 way trust between these 2 domains. I have installed an app that use Tomcat on the DomainB with integrated Windows authentication. Now when user in the DomainB access the tomacat app they get loged in without any login prompt from tomcat app but user from DomainA getting a login prompt from the tomcat app.

we have already add the url to the tomcat app to the tursted and intranet of the browser but still get the login prompt.

any suggestions to resolve this issue?

Thanks