On the Unique Solvability of a Nonlinear Reaction-Diffusion Model with Convection

Nonnegative solutions of a general reaction-diffusion model with convection are known to be unique if the reaction, convection, and diffusion terms are all Lipschitz continuous with respect to their dependence on the solution variable. However, it is also known that such a Lipschitz condition is not necessary for the unique solvability of the model if either convection or reaction is not present. We introduce monotonicity conditions which, when imposed on the reaction and convection, are sufficient for the uniqueness of all nonnegative solutions of the general model. Consideration of the model where reaction, diffusion, and convection are governed by power laws also reveals the extent to which these conditions are necessary.