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<p>The proposed work is devoted to two-dimensional problems with free boundaries that arise in mathematical modeling of problems in medicine. A new formulation of two-dimensional, two-phase problems with free boundaries is considered, and a&#xa0;simplified two-dimensional stationary Stefan problem is obtained. A system of nonlinear equations is obtained by using the general solution of the differential equation in both frozen and unfrozen areas of the biological tissue, after satisfying the boundary conditions and the conjugation conditions of the problem. The original problem is also reduced to the system of nonlinear integral equations.</p>

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Asymptotic integration of two-dimensional free boundary problems in medicine

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • F. Kh. Kudayeva

摘要

The proposed work is devoted to two-dimensional problems with free boundaries that arise in mathematical modeling of problems in medicine. A new formulation of two-dimensional, two-phase problems with free boundaries is considered, and a simplified two-dimensional stationary Stefan problem is obtained. A system of nonlinear equations is obtained by using the general solution of the differential equation in both frozen and unfrozen areas of the biological tissue, after satisfying the boundary conditions and the conjugation conditions of the problem. The original problem is also reduced to the system of nonlinear integral equations.