2022-05-20T20:27:03Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693472018-04-25T23:44:07Zhdl_2115_45007hdl_2115_116A subdifferential formulation of fourth order singular diffusion equationsKashima, Y.410A fourth order equation with singular diffusivity, which is a model of relaxation dynamics for crystalline surfaces driven by surface diffusion, is formulated. The notion of subdifferentials enables us to formulate the singular diffusion equation mathematically as a gradient flow equation in the Sobolev space of negative power H-1. The subdifferential of the singular energy in H-1 is calculated. Moreover, the speed of a special profile is calculated for one dimensional problem. It turns out that a seemingly natural free boundary formulation with facets is inconsistent with a subdifferential formulation which can be approximated by a smooth energy.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69347info:doi/10.14943/83743https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69347/1/pre598.pdfHokkaido University Preprint Series in Mathematics59812003-08engpublisher