Life span of solutions with large initial data for a semilinear parabolic system coupling exponential reaction terms

In this paper, we study a coupled systems of parabolic equations subject to large initial data. By using comparison principle and Kaplan’s method, we get the upper and lower bound for the life span of the solutions.

Differential Harnack Estimates for a Semilinear Parabolic System

In this paper, we prove differential Harnack inequalities for positive solutions of a semilinear parabolic system on hyperbolic space. We use the inequalities to construct classical Harnack estimates by integrating along space-time.