Reaction-diffusion equations are mathematical models that describe how the concentrations of substances in a system change over time due to both diffusion and reactions occurring within the system. These equations are commonly used in the field of mathematical biology to study various biological phenomena, such as the formation of spatial patterns in biological tissues, the spread of diseases, and the behavior of populations. In reaction-diffusion equations, the diffusion term accounts for the random movement of particles from areas of high concentration to areas of low concentration, while the reaction term represents the interactions between different substances that can lead to changes in their concentrations. By studying the solutions of these equations, researchers can gain insights into the underlying mechanisms driving complex biological processes and make predictions about how these systems will behave under different conditions.