论文标题
适当的火焰阵线模型的适应性和渐近性
Well-posedness and asymptotics of a coordinate-free model of flame fronts
论文作者
论文摘要
我们研究了Frankel和Sivashinsky引入的无坐标火焰阵线模型；该模型具有一个参数$α$，它与前部的不稳定有关。我们首先证明了无坐标模型的短时良好性，对于$α> 0的任何值。$ $，我们然后说，接近阈值$α\约1，$该解决方案将任意接近弱的非线性kuramoto-sivashinskin（ks）方程的解决方案，只要初始值很长。
We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter $α$ which relates to how unstable the front might be. We first prove short-time well-posedness of the coordinate-free model, for any value of $α>0.$ We then argue that near the threshold $α\approx 1,$ the solution stays arbitrarily close to the solution of the weakly nonlinear Kuramoto--Sivashinsky (KS) equation, as long as the initial values are close.
