How does one purify a garment soiled with urine at the university, given the inability to change clothes and ignorance of the exact location of the impurity, and is it permissible to delay the Dhuhr prayer until the necessary time for Asr in order to return home and purify the garment?

The Maliki school of thought does not permit delaying prayer until the الضروري (necessary) time except for certain permissible excuses, and delaying it to obtain clean clothing is not among them. Therefore, if you do not find anything other than an impure garment and fear the expiry of the Ikhtiyari (preferred) time, pray in it. If you find a clean garment before sunset, it is recommended to repeat the prayer. An impure garment is not purified except by washing it completely if the location of the impurity is indistinguishable.