In this paper we are going to show the existence of a nontrivial solution to the following model problem,

Speedup of a parallel computation is defined as Sp = T/Tp [2], where T is the sequential time of a problem and Tp is the parallel time to solve the same problem using p processors. Tp was argued to be no greater than P in [3]. However, in practice, people observed “superlinear speedup”, i.e. the speedup with P processors is greater than P. Two main reasons for superlinear speedup are shown in [...

In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.