ON ONE CONJUGATION PROBLEM FOR A FOURTH-ORDER COMPOSITE AND HYPERBOLIC TYPE EQUATION
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_11Keywords:
Conjugation problem, boundary conditions, composite type, Goursat problem, Green and Riemann function, Dirichlet problemAbstract
In the article a comprehensive study of the conjugation problem for the equation of the composite and hyperbolic types of the fourth order is carried out. When solving the conjugation problem, the methods of the theory of mixed type equations and the theory of Voltaire and Fredholm integral equations of the second kind will be used. The main problem is split into three independent problems, each of which is considered separately. In the course of solving problems, problems for second-order ordinary differential equations and problems of the Goursat type are studied. It should be noted that these ordinary differential equations arise on the line of type change and boundary conditions are found for them. The formulas for the solution of the main problem in the corresponding subdomains of the main domain are obtained. The one-valued solvability of the conjugation problem is proved.
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