The Uniqueness Criterion for a Solution to a Boundary Value Problem for the Operator (Formula presented.) with an Elliptic Operator $ A $ of Arbitrary Order

Kanguzhin B.E. Koshanov B.D.
November 2022 Pleiades Publishing

Siberian Mathematical Journal
2022 #63 Issue 6 1083 - 1090 pp.

We establish the uniqueness criterion for a solution to the operator (Formula presented.) with the Dirichlet time-dependent boundary conditionsand general boundary conditions in the space variables.The order of the differentiation operator (Formula presented.) is assumed even.Note that $ A(x,D) $ in the space variables is an arbitrary elliptic operator withsome rather general boundary operators B_j obeying the conventional Agmon conditions.The Agmon conditions ensure the existence of a complete orthonormal system of eigenfunctions (in L₂(Ω))provided that Ω isa bounded domain with sufficiently smooth boundary.

517.956 , boundary value problem , eigenfunction , entire function of exponential type , higher order elliptic operator , uniqueness of a solution

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Al-Farabi Kazakhstan National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
International University of Information Technologies, Almaty, Kazakhstan

Al-Farabi Kazakhstan National University
Institute of Mathematics and Mathematical Modeling
International University of Information Technologies

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