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Front propagation in reaction-diffusion-advection equations in homogeneous and heterogeneous media is described.

A planar differential equation x = P(x,y), y= Q(x,y) is considered, where P and Q are real-valued continuously differentiable functions on R(super2). An accessible proof for 2-dimensional systems is presented, using only elementary techniques, proving that the omega limit set of a solution to the planar system, that satisfies the Bendixson criterion is a single equilibrium or is empty.

Global existence in time or blowup in finite time of solutions to some types of reaction-diffusion systems, is examined.