Microlocal analysis and global analysis of dispersive equations

我们研究了线性色散方程解的性质(特别是解的奇性)与方程符号几何之间的关系。作为一个模型，我们考虑了具有扰动二次位势的薛定谔方程解的奇性的传播，得到了基本解的波前集在某种位势扰动下不变的充要条件。我们还得到了具有空间紧度量扰动的波动方程解的增长阶的结果(与T.Nishitani和H.Ueda共同工作)。

We studied the relation between properties of solutions (in particular, singularities of solutions) to linear dispersive equations and geometry of symbols of the equations. As a model we considered propagation of singularities of solutionsto Schrodinger equations with perturbed quadratic potentials and obtained a necessary and sufficient condition for the wavefront sets of the fundamental solutions to be invariant under some class of potential perturbations. We also obtained results on growth order of solutions to wave equations with spatially compact metric perturbations (joint work with T.Nishitani and H.Ueda).