arXiv subjects
Publications and source records attributed to Seiichi Udagawa.
We give a simple and explicit constructions of various semi-discrete surfaces and discrete $K$-surfaces in terms of the Jacobi elliptic functions using $τ$-functions. Their periodicities are also determined.
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has temperature 0 and the other has temperature 1. Suppose that the interface is uniformly of class $C^6$. We show that if the interface has a time-invariant constant temperature, then it must be a hyperplane.