We show the existence of self-similar solutions for Muskat equation. These are parameterized by 0<|s|≪1; they exact corners slope s at t=0 and become smooth in x t>0.

We define a Hesse soliton, that is, self-similar solution to the flow on Hessian manifolds. On information geometry, e-connection is important, which does not coincide with Levi–Civita one. Therefore, it interesting consider manifold flat connection call proper manifold. In this paper, we show any compact soliton expanding and non-trivial gradient proper. Furthermore, dual space of Hesse–Einste...