2023-09-29T10:12:33Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/682612022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116ON LARGE TIME BEHAVIOR OF GROWTH BY BIRTH AND SPREADON LARGE TIME BEHAVIOR OF GROWTH BY BIRTH AND SPREADGiga, YoshikazuGiga, Yoshikazu410410This is essentially a survey paper on a large time behavior of solutions of some simple birth and spread models to describe growth of crystal surfaces. The models discussed here include level-set ﬂow equations of eikonal or eikonal-curvature ﬂow equations with source terms. Large time asymptotic speed called growth rate is studied. As an application, a simple proof is given for asymptotic proﬁle of crystal grown by anisotropic eikonal-curvature ﬂow.This is essentially a survey paper on a large time behavior of solutions of some simple birth and spread models to describe growth of crystal surfaces. The models discussed here include level-set ﬂow equations of eikonal or eikonal-curvature ﬂow equations with source terms. Large time asymptotic speed called growth rate is studied. As an application, a simple proof is given for asymptotic proﬁle of crystal grown by anisotropic eikonal-curvature ﬂow.Department of Mathematics, Hokkaido UniversityDepartment of Mathematics, Hokkaido UniversityDepartmental Bulletin PaperDepartmental Bulletin Paperapplication/pdfapplication/pdfhttp://hdl.handle.net/2115/68261http://hdl.handle.net/2115/68261info:doi/10.14943/81735info:doi/10.14943/81735https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/68261/1/Giga20171129.pdfhttps://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/68261/1/Giga20171129.pdfHokkaido University Preprint Series in MathematicsHokkaido University Preprint Series in Mathematics110711071120202018-02-012018-02-01engengpublisherpublisher