Approximate solutions for nonlinear diffusion-reaction equations using the maximum principle: a case involving multiple solutions

A method for obtaining good approximate solutions for nonlinear diffusion-reaction boundary value problems, based on use of the Maximum Principle, is presented. It is applied to the case of a nonisothermal Langmuir-Hinshelwood reaction occuring in a slab catalyst, following the lumped thermal model, where there is concentration gradient within the pellet but the temperature is uniform. This problem admits multiple solutions, and it is shown that excellent estimates and rigorous error bounds for each of the multiple solutions can be obtained with ease using this method. In problems of this type involving multiple solutions, alternative methods for obtaining approximate solutions either cannot be applied or do not yield information about the error bounds.