CMMSE: Estimates of the solution and its derivatives for the semiperiodic boundary problem for pseudoparabolic equations

Myrzagali N. Ospanov, Akerke Merzetkhan

2024

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DOI 10.22541/au.172803590.02440473/v1
Data confidence 70 medium
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Abstract

In this work, the existence and uniqueness of the solution to the semiperiodic boundary problem for a third-order partial differential equation are obtained. Estimates for the solution and its derivatives have been established. To achieve this, a special substitution is used to reduce the third-order equation to a system of ordinary differential equations (ODE) and functional relations. The unique solvability of the resulting periodic boundary value problem for the ODE system is proven using the parameterization method.