Higher-Order PDEs With PCGAs: A Multi-Characteristic Approach
Assanova A.T.
2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026
This paper addresses a multi-characteristic problem for a higher-order hyperbolic partial differential equation with a piecewise-constant generalized argument. By introducing appropriate auxiliary unknowns, the original formulation is transformed into a parameter-dependent problems for a system of first-order differential equations with a piecewise-constant generalized argument and accompanying integral relations. The analysis and resolution of this auxiliary set of problems are carried out by means of the parametrization Dzhumabaev method. A novel procedure for constructing solutions on subdomains is proposed. Sufficient conditions guaranteeing the existence and uniqueness of solutions to the resulting parameter-dependent systems with piecewise-constant generalized argument are established, and algorithms for their computation are developed; their convergence is rigorously justified. On this basis, conditions ensuring the unique solvability of the initial multi-characteristic problem for higher-order partial differential equations with piecewise-constant generalized argument are derived.
higher-order partial differential equations , multi-characteristic problems , parameter-dependent multipoint problems , piecewise-constant generalized argument , solvability
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026