0次伪微分算子的谱理论及其在强迫线性波中的应用
Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves
摘要：
我们将Laure Saint-Raymond的论文“Attractor for two dimensional waves with homogeneous Hamiltonian of degree 0”的结果推广到任意维强迫线性波动方程的情形。我们证明了在2维空间中，如果能量壳在无穷远边界上的叶理是Morse-Smale，我们可以应用Brackre理论，从而得到强迫解的渐近性。我们还使用径向传播估计的极限施瓦茨分布的波前集的特征。
英文摘要：
We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0" written with Laure Saint-Raymond to the case of forced linear wave equations in any dimension. We prove that, in dimension 2,if the foliation on the boundary at infinity of the energy shell is Morse-Smale, we can apply Mourre's theory and hence get the asymptotics of the forced solution. We also characterize the wavefrontsets of the limit Schwartz distribution using radial propagation estimates.
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