Global existence for a vector-valued nonlinear heat equation (Q1869968)

The paper studies global existence, uniqueness and nonnegativity of classical solutions to the semilinear parabolic system \[ u_t=\Delta u+f(\nabla u,\nabla v),\qquad v_t=\Delta v+g(\nabla u,\nabla v) \] in \({\mathbb R}^N\times {\mathbb R}_+.\)