Numerical Simulation of Burning Front Propagation

In the context of a numerical experiment, it is shown that the switching wave described by the reaction–diffusion equation can be delayed at a medium inhomogeneity with a thickness $\Delta$ and amplitude $\Delta\beta$ for a finite time $\tau=\tau(\Delta\beta,\Delta)$ up to a complete stop at it $\tau=\infty$. Critical values $\Delta\beta_c$ and $\Delta_c$ corresponding to the autowave stop are found. The similarity laws are established $\tau\sim(\Delta_c-\Delta)^{-\gamma_{\Delta}}$, $\tau\sim(\Delta\beta_c-\Delta\beta)^{-\gamma_{\beta}}$ and critical indexes $\gamma_{\Delta}$, $\gamma_{\beta}$ are found. The similarity law is established for critical values of amplitude and width of the inhomogeneity corresponding to the autowave stop $\Delta\beta_c\sim\Delta_c^{-\delta}$, where $\delta\approx1$.