In this paper, we are interested in the study of a degenerate reaction-diffusion model, where we prove the existence of positive maximal and minimal solutions, including the uniqueness of the positive solution. The technique used is mainly based on the method of upper and lower solutions.

"In this paper, we show the existence of continuous positive solutions of a class of nonlinear parabolic reaction di usion systems with initial conditions using techniques of functional analysis and potential analysis."

We study the existence of weak solutions for a parabolic reaction diffusion model applied in Quenching endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The techniques used are based on energy estimates to approach nonsingular problems and uniform control on the set where singularities are localizing.