Final_submission

The issue of nutrient deficiency in plants and an effective uptake of nutrients from the soil is a problem affecting crop-focused industries in the modern age. This project is concerned with expanding an existing model for nutrient extraction using one exudate-producing root into a two root system. First, a set of boundary conditions is added to model another root and experiment with the proximity of two identical roots and the exudation rate with the intention to model intercropping. Then we derive a system with two exudates produced by two roots which we use for further numerical experiments with the model's parameters. Overall, we find that planting at a close enough distance that the zones of root influence interact is key to encouraging a mutually beneficial relationship between roots. The results also show that for higher nutrient uptake, increased exudation rate of the roots and increased diffusion and buffer power of the nutrient are important, along with decreased buffer power and diffusion of the exudates. Finally, an analysis of the system provides us with a proof of existence of a solution.