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

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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.