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<p>Phase transition problems for isothermal surfaces play an important role in various fields of science and technology. Solving such problems allows solving complex physical problems, optimizing technological processes, developing computational methods and gaining new knowledge. In order to determine the field of isotherms, the problem of conjugation with a&#xa0;free surface is obtained in this work. A method is proposed for the transition of the problem of determining the temperature field to the problem of determining isothermal surfaces. The monotonicity of the differentiation operator is proved, which made it possible to formulate and prove the uniqueness theorem of the Stefan problem for the field of isotherms. The uniqueness theorem for solving the problem with phase transitions for isothermal surfaces is proved. The results obtained will allow us to investigate the relationship between physical parameters and biological effects. The results will be used in cryosurgery, cryopreservation, cryotherapy, hypothermia.</p>

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Tasks with free boundaries for isothermal surfaces with low-temperature effect on biological tissues

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • I. V. Veshneva,
  • F. Kh. Kudayeva,
  • A. R. Bechelova

摘要

Phase transition problems for isothermal surfaces play an important role in various fields of science and technology. Solving such problems allows solving complex physical problems, optimizing technological processes, developing computational methods and gaining new knowledge. In order to determine the field of isotherms, the problem of conjugation with a free surface is obtained in this work. A method is proposed for the transition of the problem of determining the temperature field to the problem of determining isothermal surfaces. The monotonicity of the differentiation operator is proved, which made it possible to formulate and prove the uniqueness theorem of the Stefan problem for the field of isotherms. The uniqueness theorem for solving the problem with phase transitions for isothermal surfaces is proved. The results obtained will allow us to investigate the relationship between physical parameters and biological effects. The results will be used in cryosurgery, cryopreservation, cryotherapy, hypothermia.