标题： 准等压模型的线性烧蚀增长率研究 显示英文标题

标题： Study of the linear ablation growth rate for the quasi isobaric model of Euler equations with thermal conductivity

摘要： 在本文中，我们研究与Kull-Anisimov [14]的准等压近似下的二维Euler方程组相关的线性系统。 该模型用于研究烧蚀前沿不稳定性，这出现在惯性约束聚变问题中。 该物理系统包含一个混合区域，在该区域中气体的密度迅速变化，并将L0表示为相关的特征长度。 方程组在稳态解附近进行线性化，每个扰动量都使用正常模方法来表示。 得到的线性系统不是自伴的，阶数为5，其系数依赖于x和物理参数$\alpha, \beta$。 我们使用ODE系统在$\pm \infty$处衰减的解的严格构造来计算与此线性系统相关的Evans函数。 我们证明，当$\alpha$很小时，线性化系统没有有界解。 显示英文摘要

摘要： In this paper, we study a linear system related to the 2d system of Euler equations with thermal conduction in the quasi-isobaric approximation of Kull-Anisimov [14]. This model is used for the study of the ablation front instability, which appears in the problem of inertial confinement fusion. This physical system contains a mixing region, in which the density of the gaz varies quickly, and one denotes by L0 an associated characteristic length. The system of equations is linearized around a stationary solution, and each perturbed quantity is written using the normal modes method. The resulting linear system is not self-adjoint, of order 5, with coefficients depending on x and on physical parameters $\alpha, \beta$. We calculate Evans function associated with this linear system, using rigorous constructions of decreasing at $\pm \infty$ solutions of systems of ODE. We prove that for $\alpha$ small, there is no bounded solution of the linearized system.