Blow-up solutions of cubic differential systems

We investigate the existence problem for blow-up solutions of cubic differential systems. We find sets of initial values of the blow-up solutions. We also discuss a method of finding upper estimates for the blow-up time of these solutions. Our approach can be applied to systems of partial differential equations. We apply this approach to the Cauchy–Dirichlet problem for systems of semilinear heat equations with cubic nonlinearities. © 2007 Published by Elsevier Inc.