On the existence and coercive estimates of solutions to the Dirichlet problem for a class of third-order differential equations - Suleimbekova, A.O.; Musilimov, B.M. (Академик Е.А. Бөкетов атындағы Қарағанды университеті, 2024)
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 à 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.
Үшінші ретті дифференциалдық теңдеулердің бір класы үшін Дирихле есебі шешімдерінің бар болуы және коэрцитивті бағалаулары туралы
О существовании и коэцитивных оценках решений задачи Дирихле для одного класса дифференциальных уравнений третьего порядка
Keywords: resolvent; third order differential equation; Dirichlet problem; coercive estimates