Minimum wave speed and uniqueness of monotone mono-stable traveling waves

Reaction-diffusion equations are used in many fields, including biology, chemistry, and physics. The solutions of reaction diffusion equations have many different forms. Traveling wave solutions are one important type. Monotone traveling waves are used to model many physical problems. One example is Fisher's equation, which uses traveling waves to study the spread of favorable genes. Zel'dovich's equation uses wave propagation to study the movement of flames caused by explosions. There are other applications in many areas of science.;The speed of a traveling wave determines how quickly it converges to a stable state. It is known that a traveling wave solution u( x, t) = U(k · x + ct) to a reaction diffusion equation 6ux,t 6t = Deltau(x, t)+f( u(x, t)) exists if and only if the wave speed c is greater than some value c* . This value is known as the minimum wave speed. Using the Lotka-Volterra competition model as an example, a method is developed for determining this minimum wave speed. In the example model, the exact minimum wave speed is determined. Furthermore, the method could be applied to other models. A related problem is the question of uniqueness. This problem of uniqueness is solved for the general case, including time delay.