Uniquely solvable problems for abstract Legendre equation

For loaded abstract Legendre equation we find sufficient conditions of solvability of the Cauchy problem and the boundary control problem. We also consider nonlocal problem that contains fractional integral of a function with respect to another functio

Solvability of degenerating hyperbolic differential equations with unbounded operator coefficients

We consider initial value problems for a number of hyperbolic equations with a power-law degeneracy and with operator coefficients in a Banach space and establish sufficient conditions for the unique solvability of these problems in terms of the coefficients of the equation, the degeneracy order, and the initial element

Uniqueness criterion for solutions of nonlocal problems on a finite interval for abstract singular equations

For abstract singular equations, nonlocal problems belonging to the class of ill-posed problems are considered. A uniqueness criterion for solutions is establishe

A family of singular differential equations

A family of singular differential equations with variable coefficients and parameter k ∈ R is introduced into the consideration. The properties inherent in all differential equations of this family are investigated and theorems on the solvability of a number of initial problems for the considered family are formulate

Solution of a boundary value problem for velocity-linearized Navier-Stokes equations in the case of a heated spherical solid particle settling in fluid

Assuming that the fluid viscosity is an exponential-power function of temperature, a boundary value problem for the Navier-Stokes equations linearized with respect to velocity is solved and the uniqueness of the solution is proved. The problem of a nonuniformly heated spherical solid particle settling in fluid is considered as an applicatio

Differences of craniotype distribution and types of face among apparently healthy men from different regions of Ukraine

Established peculiarities of craniotype distribution and types of face in somatically healthy men depend on regional affiliation. In all regions of Ukraine, markedly greater brachycephaly percentage was found, indicating the trend towards brachycephalisation and prevalence of men with narrow and very narrow face, which confirms gracilisation. The study showed a small number of regional differences in the distribution of specific types of the skull and face, indicating that the population of Ukraine is very homogeneous in anthropological composition and none of the presented Ukrainian regional types is beyond anthropological type, common to people in general

Inverse problems for evolution equations with fractional integrals at boundary-value conditions=Обратные задачи для эволюционных уравнений с дробными интегралами в краевых условиях

yesБелГУДоказательство однозначной разрешимости обратной задачи для абстрактного дифференциального уравнения первого порядка с интегралом дробного порядка в граничном условии. Показано, что разрешимость зависит от распределения нулей функции Миттаг-Леффлера и спектра оператора, входящего в уравнени

Correctness of Cauchy-Type Problems for Abstract Differential Equations with Fractional Derivatives = Корректная разрешимость проблем для абстрактных дифференциальных уравнений с мелкими дробными производными

yesBSUДоказывается равномерная корректность задачи типа Коши с двумя дробными производными и ограниченным оператором A. Для неограниченного оператора A приводится критерий равномерной корректност

On an Inverse Problem for an Abstract Differential Equation of Fractional Order=Об одной обратной задаче для абстрактного дифференциального уравнения дробного порядка

yesБелГУДоказательство однозначной разрешимости обратной задачи для абстрактного дифференциального уравнения, содержащего дробные производные. Показано, что разрешимость зависит от распределения нулей функции Миттаг-Леффлера и спектра оператора, входящего в уравнени

Correctness of Cauchy-Type Problems for Abstract Differential Equations with Fractional Derivatives = Корректная разрешимость проблем для абстрактных дифференциальных уравнений с мелкими дробными производными

We prove the uniform well-posedness of a Cauchy-type problem with two fractional derivatives and a bounded operator A. For an unbounded operator A, we give a criterion for the uniform correctnessyesBS