2023-03-26T05:42:45Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693582022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116LOCAL SOLVABILITY OF A CONSTRAINED GRADIENT SYSTEM OF TOTAL VARIATIONGIGA, YOSHIKAZUKASHIMA, YOHEIYAMAZAKI, NORIAKIopen access410A 1¡harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in RN is formulated by use of subdifferentials of a singular energy - the total variation. An abstract convergence result is established to show that solutions of approximate problem converge to a solution of the limit problem. As an application of our convergence result a local-in-time solution of 1¡harmonic map flow equation is constructed as a limit of the solutions of p¡harmonic (p > 1) map flow equation, when the initial data is smooth with small total variation under periodic boundary condition.Department of Mathematics, Hokkaido University2003-10-18engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83754http://hdl.handle.net/2115/6935810.14943/83754Hokkaido University Preprint Series in Mathematics609132https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69358/1/pre609.pdfapplication/pdf240.47 KB2003-10-18