Study of partial differential equations and tomography by microlocal and discrete methods

我们用微局部离散方法研究了偏微分方程和层析成像的各种问题。特别地，我们通过确定广义抛物面区域的临界指数，得到了对数非线性半线性热方程解爆破临界指数的新的有趣的结果，以及研究解的非唯一性的一种方法--2投影层析的解集的切换图，借助于理论考虑和计算机实验，将它们列举到20阶，得到了有趣的结果。

We studied on various problems of partial differential equations and tomography by means of microlocal and discrete approach. Especially we got new interesting results on the critical exponent of blowup of semilinear heat equation with logarithmic nonlinearity by determining the critical exponent for generalized paraboloidal domain, and on the switching graph of solution sets of 2 projection tomography which is a means of studying non-uniqueness of solution, by enumerating them up to order 20 with aid of theoretical consideration and computer experiment.