one way is to write an abstract test case that corresponds to your abstract class, then write concrete test cases that subclass your abstract test case. do this for each concrete subclass of your original abstract class (i.e. your test case hierarchy mirrors your class hierarchy). see Test an interface in the junit recipies book: http://safari.informit.com/9781932394238/ch02lev1sec6. https://www.manning.com/books/junit-recipes or https://www.amazon.com/JUnit-Recipes-Practical-Methods-Programmer/dp/1932394230 if you don't have a safari account.
also see Testcase Superclass in xUnit patterns: http://xunitpatterns.com/Testcase%20Superclass.html