Boundary value problem for the third-order equation with multiple characteristics

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Annals of Mathematics and Physics volume6-issue1 articles
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Submitted: December 23, 2022
Published: Jan 6, 2023
DOI: 10.17352/amp.000067
Keywords:
Boundary value problems, Third order equation, Multiple characteristics, Quadratic forms, Uniqueness of solution, The existence of solution, Green's function, Potential theory, Fundamental solution

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Djumaniyazova Khilola Atamuratovna
Higher and applied mathematics, Tashkent Institute of Finance, Uzbekistan
Khashimov Abdukomil Risbekovich*
Higher and applied mathematics, Tashkent Institute of Finance, Uzbekistan

Abstract

The article constructs a unique solution to a tertiary-order equation with multiple characteristics with boundary conditions that include all possible local boundary conditions. The uniqueness of the solution of boundary value problems is proved by the method of integral equations using the sign-definiteness of quadratic forms. When proving the existence of a solution to the problem, Green's function method, the theory of integral equations and potentials are used.

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Article Details

Atamuratovna, D. K., & Risbekovich, K. A. (2023). Boundary value problem for the third-order equation with multiple characteristics. Annals of Mathematics and Physics, 6(1), 001–003. https://doi.org/10.17352/amp.000067
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Copyright (c) 2023 Atamuratovna DK, et al.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Abdul-Majid Wazwaz. Soliton solutions for the fifth-order KdV equation and the Kawahara equation with time-dependent coefficients. Physica Scripta. 2010; 82:035009; 4. doi: 10.1088/0031-8949/82/03/035009.

Freire Igor Leite and Julio Cesar Santos Sampaio. Nonlinear self-adjointness of a generalized fifth-order KdV equation. Journal of Physics A: Mathematical and Theoretical. 2012; 45:032001; 7.

Igor Leite Freire. New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order. Preprint: arXiv: 2012;3955vl.

Larkin NA. Modified KdV equation with a source term in a bounded domain. Mathematical Methods in the Applied Sciences. 2006; 29:751-765.

Larkin NA, Luchesi J. General mixed problems for KdV equation on bounded intervals. Electronic Journal of Differential Equations. 2010; 2010:168; 1-17.

Wengu Chen, Zihua Guo. Global well-posedness and I method for the fifth order Korteveg - de Vries equation. Journal d’analyse mathematique. 2011; 114:121-156.

Marin Marin. Generalized solutions in the elasticity of micropolar bodies with voids. Revista de la Academia Canaria de Ciencias: Folia Canariensis Academiae Scientiarum, 1996; ISSN 1130-4723: 8; Nº 1:101-106.

Marin Marin Contributions on uniqueness in thermoelastodynamics on bodies with voids, Ciencias matemáticas, (Havana). 1998; 16(2):101-109.

Marin M, Oechsner A, Craciun EM. A generalization of the Saint-Venant’s principle for an elastic body with dipolar structure Continuum Mechanics nad Thermodynamics. 2020; 32(1):269-278.

Оleynik ОА. On the behavior of solutions of linear parabolic systems of differential equations in unbounded domains. Advances in Mathematical Sciences. 1975; 30:2; 219-220.

Оleynik ОА, Iosifyan GA. A priori estimates for solutions of the first boundary value problem for the system of elasticity equations and their applications. Advances in Mathematical Sciences. 1979; 32: № 5; 193.

Оleynik ОА, Iosifyan GA. On the Saint-Venant principle in the plane theory of elasticity. Reports of the Academy of Sciences. 1978; V-239:3; 530.

Cattabriga L. Un problema al per una equazione parabolica di ordine dispari. Annali della Souola Normale Sup. di Pisa a mat. 1959; 13:2; 163-203.

Khashimov AR. A non-local problem for a non-stationary equation of the third order of a composite type with a general boundary condition. West. Myself. Tech. Un-ta, Ser. Phys.-Math. Sciences. 2020; 1(24): 187-198.

Khashimov AR, Dana Smetanova. Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions. Axioms. 2021; 10:110. https://doi.org/10.3390/axioms10020110.