Abstract: The author considered the properties of solutions of initial boundary value problems for quasilinear parabolic systems from combustion theory, and obtained sufficient conditions for the existence and nonexistence of global solutions by using energy estimation method, Jensen inequality and Gronwall inequality. The results show that there is a global non negative solution to the problem if the parameter m in the equation is odd and the initial value satisfies appropriate integrability conditions; and the solution of the problem will blow up at a finite time if m is even and the integral of the initial value is suitably large.

Key words: global boundedness, parabolic system, combustion theory, blowup