Do the times for Dhuhr and Asr overlap such that the Dhuhr prayer is performed as adaa' (on time) if the time for Asr has begun and it has not yet been prayed?

It is not permissible to delay the Dhuhr prayer beyond its optional time. Whoever does so without a valid excuse has committed a sin. According to the Malikis and those who agree with them, his prayer is considered on-time performance (adaa'), while according to the majority of scholars, it is considered a make-up (qadaa').