Local and global existence for quasilinear parabolic systems with a strongly nonlinear source

We study the Cauchy problem for quasilinear parabolic systems with a strongly nonlinear source on the assumptions that the initial values are taken in the sense of Lloc1(RN). We obtain the local existence, global existence and nonexistence of solutions. Particularly, in the case of global solvability, some exact estimates of a solution are obtained.