Differential Harnack estimates for a semilinear parabolic system (Q2422468)

In this paper, the author considers the following problem: \[ f_t= \Delta f + e^{\mu t}g^p, \] \[ g_t= \Delta g + e^{\nu t}f^q, \] where \(p\), \(q\), \(\mu\) and \(\nu\) are suitable costants. By following the celebrated Li and Yau approach, the author proves differential Harnack inequalities for positive solutions of a semilinear parabolic system on hyperbolic space. These inequalities are used to construct classical Harnack estimates by integrating along space-time.