On the existence and coercive estimates of solutions to the Dirichlet problem for a class of third-order differential equations


Үшiншi реттi дифференциалдық теңдеулердiң бiр класы үшiн Дирихле есебi шешiмдерiнiң бар болуы және коэрцитивтi бағалаулары туралы
О существовании и коэрцитивных оценках решений задачи Дирихле для одного класса дифференциальных уравнений третьего порядка
Suleimbekova A.O. Musilimov B.M.
2024E.A. Buketov Karaganda University Publish house

Bulletin of the Karaganda University. Mathematics Series
2024#114Issue 2178 - 185 pp.

As you know, the third order partial differential equation is one of the basic equations of wave theory. For example, in particular, a linearized Korteweg-de Vries type equation with variable coefficients models ion-acoustic waves into plasma and acoustic waves on a crystal lattice. In this paper, the properties of solutions of а class of the third order degenerate partial differential equations with variable coefficients given in a rectangle were studied. Sufficient conditions for the existence and uniqueness of a strong solution have been established. Note that the solution of the degenerate equation does not retain its smoothness, therefore, these difficulties in turn affect the coercive estimates.

coercive estimates , Dirichlet problem , resolvent , third order differential equation

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Department of Mathematics, M.Kh. Dulaty Taraz Regional University, 7 Suleymenov street, Taraz, 080000, Kazakhstan
Department of Mathematics, M.Kh. Dulaty Taraz Regional University, 7 Suleymenov street, Taraz, 080000, Kazakhstan

Department of Mathematics
Department of Mathematics

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