In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and ...

the galerkin finite element method is used to solve the three dimensional continuity, momentum and energy equations for laminar newtonian and power-law model non-newtonian flow through horizontal circular tube. the governing equations are non-dimensionalized with respect to specific variables and converted into algebraic equations using appropriate elements. to accelerate convergence a combinat...

We consider the fixed interval smoothing problem for data from linear or nonlinear models where there is a priori information about the boundary values of the state process. The nonlinearities and boundary values preclude a stochastic approach so instead we use a least squares methodology. The resulting variational equations are a coupled system of ordinary differential equations for the state ...

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

Exponential stability analysis via Lyapunov method is extended to the one-dimensional heat and wave equations with time-varying delay in the boundary conditions. The delay function is admitted to be time-varying with an a priori given upper bound on its derivative, which is less than 1. Sufficient and explicit conditions are derived that guarantee the exponential stability. Moreover the decay r...

In this paper, we study boundary value problems for differential equations involving Caputo derivative of order α ∈ (2, 3) in Banach spaces. Some sufficient conditions for the existence and uniqueness of solutions are established by virtue of fractional calculus, a special singular type Gronwall inequality and fixed point method under some suitable conditions. Examples are given to illustrate t...

Since Al-Salam [1] and Agarwal [2] introduced the fractional q-difference calculus, the theory of fractional q-difference calculus itself and nonlinear fractional q-difference equation boundary value problems have been extensively investigated by many researchers. For some recent developments on fractional q-difference calculus and boundary value problems of fractional q-difference equations, s...

A collocation method with the modified equilibrium on line method (ELM) forimposition of Neumann and Robin boundary conditions is presented for solving the two-dimensionalacoustical problems. In the modified ELM, the governing equations are integrated over the lines onthe Neumann (Robin) boundary instead of the Neumann (Robin) boundary condition equations. Inother words, integration domains are...

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...