Monotonicity conjecture for flame-front velocity and reaction width

Let $c^*(\theta,\Lambda,\alpha)$ denote the velocity of propagation and let $R^*(\theta,\Lambda,\alpha)$ denote the reaction width, where $\theta$ is the ignition temperature, $\Lambda$ is the ratio of molecular to thermal diffusivity, and $\alpha\in(0,1)$ is the reaction order. Monotonicity conjecture. The velocity $c^*(\theta,\Lambda,\alpha)$ is a decreasing function of all of its arguments, whereas the reaction width $R^*(\theta,\Lambda,\alpha)$ is a decreasing function of $\theta$ and an increasing function of $\Lambda$ and $\alpha$. The conjecture is suggested by asymptotic analysis, physical reasoning, and numerical observations; no resolution is given in the supplied text.