In the context of the large thermal-expansion approximation, we derive an equation describing flame front dynamics under conditions of Darrieus-Landau instability. We show that the second-order theory leads to system of two evolution equations for the flame front perturbations and for the potential of the unburned mixture flow. In the limiting case of long evolution, the system of equations can be reduced to one equation with respect to the additive variable that is the sum of the front perturbations and the flow potential. The equation with respect to the additive variable at large gas expansion coefficients has the form of the Sivashinsky equation obtained for the case of small gas expansion coefficients.

在大热膨胀近似的背景下，我们推导出了一个描述 Darrieus-Landau 不稳定性条件下火焰前沿动力学的方程。我们表明，二阶理论导致了火焰前沿扰动和未燃烧混合物流势的两个演化方程组。在长演化的极限情况下，方程组可以简化为一个关于附加变量的方程，该变量是前沿扰动和流动势的总和。关于在大气体膨胀系数下的加性变量的方程具有在小气体膨胀系数的情况下获得的 Sivashinsky 方程的形式。