Competition between languages affects the lives of people all over the globe, and a huge number of languages are at risk of extinction. In this work, statistical physics is applied to modelling the decline of one language in competition with another. A model from the literature is used and adapted to model the interactions among speakers in a population distribution over time, and is applied to historical data for Cornish and Welsh. Visual, geographical models show the simulated decline of the real languages studied, and a number of qualitative and quantitative features from the historical data are captured by the model. The applicability of the model to further real situations is discussed, as well as adaptations that would be needed to better take account of migration and population dynamics.