Solvability Of Nonlocal Problem Research Articles

BOUNDARY VALUE PROBLEM WITH A NONLOCAL BOUNDARY CONDITION OF INTEGRAL FORM FOR A MULTIDIMENSIONAL EQUATION OF IV ORDER

The aim of this paper is to study the solvability of solution of non-local problem with integral condition in spatial variables for high-order linear equation in the classe of regular solutions (which have all the squaredderivatives generalized by S.L. Sobolev that are included in the corresponding equation). It is indicated that at first similar problems were studied for high-order equations either in the one-dimensional case, or under certain conditions of smallness by the value of T. A list of new works for the multidimensional case is also given. In this paper, we present new results on the solvability of non-local problem with integral spatial variables for high-order equation a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions by the value T; however, this condition exists for the kernel K(x; y; t). The research method is based on obtaining a priori estimates of the solution of the problem, which implies its existence and uniqueness in a given space.

Нелокальные задачи с интегральным смещением для параболических уравнений высокого порядка

The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described.

Нелокальные задачи с интегральным условием для дифференциальных уравнений третьего порядка

Работа посвящена исследованию разрешимости нелокальных задач с интегральным по переменной $t$ условием для уравнений $$ u_{tt}+(\alpha\frac{\partial}{\partial t}+\beta)\Delta u=f(x,t) $$ ($\alpha$, $\beta$ - действительные постоянные, $\Delta$ - оператор Лапласа по пространственным переменным). Для изучаемых задач доказываются теоремы существования и единственности регулярных решений (имеющих все обобщенные по С. Л. Соболеву производные, входящие в уравнение).

Solvability of Nonlocal Problems for Systems of Sobolev-Type Differential Equations with a Multipoint Condition

We consider a nonlocal problem for a system of loaded differential equations of the Sobolev type with a multipoint constraint. By introducing additional unknown functions, we reduce the problem under consideration to an equivalent problem consisting of a nonlocal multipoint problem for a system of loaded hyperbolic equations of the second order with functional parameters and integral correlations. We propose algorithms for solving the equivalent problem. Moreover, we establish conditions for the well-posedness of the nonlocal multipoint problem for the system of loaded hyperbolic equations of the second order and conditions for the existence of a unique classical solution to the nonlocal problem for the system of differential equations of the Sobolev type with a multipoint constraint.

Nonlocal Problem for the Abstract Bessel—Struve Equation

We find sufficient conditions for the unique solvability of nonlocal problem for the abstract Bessel—Struve differential equation. Both nonlocal conditions are written with the help of Krdelyi—Kober operators.

О разрешимости нелокальной задачи для системы дифференциальных уравнений соболевского типа с многоточечным условием

О разрешимости нелокальной задачи для системы дифференциальных уравнений соболевского типа с многоточечным условием

Nonlocal problems with integral conditions for elliptic equations

ABSTRACTThe article consists of three parts. In the first part, we study nonlocal problems for Poisson equations in the cylinder (Ω is a bounded domain and Δ is the Laplacian with respect to the variables , …, ) by defining the integral condition and some natural boundary conditions on the lower base and on the lateral surfaces of the cylinder Q. The second part of the article is devoted to the study of the solvability of nonlocal problems with integral conditions for elliptic equations with spectral parameter. In the third part, we study some generalizations of the problems presented in the first two parts – to the case of more general integral conditions, to the case of operator-differential equations, and to the case of quasielliptic equations

On Solvability of Nonlocal Problem for Loaded Parabolic-Hyperbolic Equation

We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains the partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville of values of function derivative on the degeneration line and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

Abstract Euler–Poisson–Darboux equation with nonlocal condition

We find conditions for the unique solvability of nonlocal problems for abstract differential equation of the Euler–Poisson–Darboux equation. Nonlocal conditions contain either Erdelyi–Kober operator or Riemann–Liouville fractional integration operator.

Cauchy Problem for Autonomous Quasilinear Parabolic Pseudodifferential Equations with Deviating Argument

We use the step-by-step method to prove the solvability of nonlocal problem for an autonomous quasilinear parabolic pseudodifferential equation with nonsmooth symbols and deviations of the argument.

On the solvability of nonlocal problems for elliptic systems in infinite angles

On the solvability of nonlocal problems for elliptic systems in infinite angles