Conditions for positivity of solutions of a class of dissipative partial differential equations Original Research Article

It is a difficult problem to establish useful results on positivity of solutions of semilinear dissipative partial differential equations containing differential operators of order higher than that of the Laplacian. Positivity results are of importance in some fields of applied mathematics, such as in mathematical biology, where positivity of solutions is often needed because of the modelling application. In this paper, we first obtain ladder estimates for a particular class of semilinear dissipative partial differential equations, through which one can find conditions which will at least ensure that solutions are eventually (i.e., asymptotically) positive.