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<p>In this paper, we present a computational model for solving the first boundary-value problem for a mixed differential equation in a spatially two-dimensional case using an implicit finite-difference scheme. For a fourth-order equation, we use two different second-order operators that are similar to a one-dimensional mixed heat transfer conductivity operator in the spatial variable, generalizing the purely hyperbolic case and used in mathematical modeling of the shutdown process for an electric arc. The well-posedness of the boundary-value problem is proved.</p>

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THE FIRST BOUNDARY-VALUE PROBLEM FOR SOME MIXED EQUATIONS OF HEAT TRANSFER OF THE SECOND AND FOURTH ORDER

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • V. N. Khankhasaev,
  • V. M. Plastinina

摘要

In this paper, we present a computational model for solving the first boundary-value problem for a mixed differential equation in a spatially two-dimensional case using an implicit finite-difference scheme. For a fourth-order equation, we use two different second-order operators that are similar to a one-dimensional mixed heat transfer conductivity operator in the spatial variable, generalizing the purely hyperbolic case and used in mathematical modeling of the shutdown process for an electric arc. The well-posedness of the boundary-value problem is proved.