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Abstract <p>By the method of reducing the order of the equation, the boundary value problem is posed for a third-order mixed parabolic-hyperbolic equation and reduced to the Tricomi problem for a second-order mixed parabolic-hyperbolic equation. The solvability of the problem is reduced to the solvability of the Volterra integral equation of the second kind with two independent variables. After determining the trace of the function and its first-order derivatives on the line of change of type, the solution to the problem is completely determined in the parabolic and hyperbolic regions.</p>

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Boundary Value Problems for a Mixed Third-Order Parabolic-Hyperbolic Equation with Lower Terms

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • A. S. Sopuev,
  • B. Sh. Nuranov

摘要

Abstract

By the method of reducing the order of the equation, the boundary value problem is posed for a third-order mixed parabolic-hyperbolic equation and reduced to the Tricomi problem for a second-order mixed parabolic-hyperbolic equation. The solvability of the problem is reduced to the solvability of the Volterra integral equation of the second kind with two independent variables. After determining the trace of the function and its first-order derivatives on the line of change of type, the solution to the problem is completely determined in the parabolic and hyperbolic regions.