A note on well-posedness of source identification elliptic problem in a Banach space

We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in H¨older norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained

On a coupled PDE model for image restoration

In this paper, we consider a new coupled PDE model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. This is a rough draft, and the final version of the paper will contain a modelling part and numerical experiments

О разрешимости одной альфа-модели движения жидкости с памятью

We study a weak solvability of one alpha-model for non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the considered alpha-model coincides with the classical model describing the motion of a fluid with memory. This model takes into account the fluid's memory along the trajectory. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero.В работе исследуется существование слабых решений одной альфа-модели неньютоновской гидродинамики. Если параметр альфа равен нулю, то указанная альфа-модель совпадает с классической моделью, описывающей движение жидкости с памятью. Данная модель учитывает память среды вдоль траектории движения. Кроме того, устанавливается, что при стремлении параметра альфа к нулю решения рассматриваемой альфа-модели стремятся к решениям классической модели

On Solvability of a Fluid Flow Alpha-Model With Memory

We study weak solvability of an alpha-model in non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the alpha-model coincides with the classical one describing a fluid flow with memory. This model takes into account fluid’s memory along trajectories of movement. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero. © 2018, Allerton Press, Inc

On Solvability of a Fluid Flow Alpha-Model With Memory

We study weak solvability of an alpha-model in non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the alpha-model coincides with the classical one describing a fluid flow with memory. This model takes into account fluid’s memory along trajectories of movement. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero. © 2018, Allerton Press, Inc

О разрешимости одной альфа-модели движения жидкости с памятью

We study a weak solvability of one alpha-model for non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the considered alpha-model coincides with the classical model describing the motion of a fluid with memory. This model takes into account the fluid's memory along the trajectory. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero.В работе исследуется существование слабых решений одной альфа-модели неньютоновской гидродинамики. Если параметр альфа равен нулю, то указанная альфа-модель совпадает с классической моделью, описывающей движение жидкости с памятью. Данная модель учитывает память среды вдоль траектории движения. Кроме того, устанавливается, что при стремлении параметра альфа к нулю решения рассматриваемой альфа-модели стремятся к решениям классической модели

On the solvability of an alpha model of the motion of a fluid with memory

The authors consider a system describing a viscoelastic fluid with memory effects, regularized by introducing the so-called alpha modifications of the fluid velocity. They prove existence of weak solutions in the two- and three-dimensional domains, and convergence of solutions to those of the classical hydrodynamical model when the parameter alpha tends to 0

A note on well-posedness of source identification elliptic problem in a Banach space

We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in Holder norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained

On well-posedness of source identification elliptic problem with nonlocal boundary conditions

We study the well-posedness of the source identification problem for the two dimensional elliptic differential equation with nonlocal boundary conditions. Applying operator approaches, the exact estimates for the solution of this problem in Hölder norms are established. © 2021 Author(s)

A note on well - posedness of source identification elliptic problem in a Banach space

We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in Ho¨lder norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained.Исследована проблема идентификации источника для эллиптического дифференциального уравнения в банаховом пространстве. Получены точные оценки для решения задачи идентификации источника в нормах Хелдера. В приложениях исследованы четыре эллиптических задачи идентификации источника. Получены оценки устойчивости и коэрцитивной устойчивости для решения задач идентификации источника для эллиптических уравнени