NAKANO NAOTO    Department   Graduate School  , Graduate School of Advanced Mathematical Sciences    Position   Associate Professor (non-tenured)
Research Period	2013/04～2016/03
Research Topic	A study Research of mathematical analysis and numerical analytical a non-linear continuum with density gradient-dependent stress
Research Type	KAKENHI Research
Consignor	Japan Society for the Promotion of Science
Research Program Type	Grant-in-Aid for Young Scientists (B)
KAKENHI Grant No.	25870005
Responsibility	Representative Researcher
Representative Person	NAKANO Naoto
Details	This research project studied mathematical analysis and numerical analysis for a continuum model with density gradient-dependent stress. This model is represented by a system of partial differential equations for the density function and the velocity vector field of the continuum. Since the principal terms include degenerate non-linear terms with respect to the density, it is difficult to prove the well-posedness of, for example, an initial-boundary value problem for this model in general. We focused on a characteristic steady solution specific to this model, which is so called cycloid solution, to deepen understandings of characteristic properties of a continuum behaviour described by this model. Here, by performing mathematical and numerical analysis, we obtained some well-posedness results and resolved singular profiles of the solutions.