A Crank-Nicolson type minimization scheme for a hyperbolic free boundary problem

DOI DOI 9 References
  • Yoshiho Akagawa
    National Institute of Technology, Gifu College, Motosu, Gifu, 501-0495, Japan
  • Elliott Ginder
    Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakanoku, Tokyo, 164-8525, Japan
  • Syota Koide
    Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa, 920-1192, Japan
  • Seiro Omata
    Institute of Science and Engineering, Kanazawa University, Kanazawa, Ishikawa, 920-1192, Japan
  • Karel Svadlenka
    Graduate School of Science, Kyoto University, Sakyoku, Kyoto, 606-8502, Japan

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<jats:p xml:lang="fr"><p style='text-indent:20px;'>We consider a hyperbolic free boundary problem by means of minimizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free boundaries, which is an essential property for numerical calculations. The existence and regularity of minimizers is shown and an energy estimate is derived. These results are then used to show the existence of a weak solution to the free boundary problem in the 1-dimensional setting.</p></jats:p>

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