This paper concerns the two-dimensional NavierStokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞(∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c1G + c2Re, where G is the Grashof number and Re the Reynolds number.

A micromixer with unbalanced three-split rhombic sub-channels was proposed, and analyses of the mixing and flow characteristics of this micromixer were performed in this work. Three-dimensional Navier-Stokes equations in combination with an advection-diffusion model with two working fluids (water and ethanol) were solved for the analysis. The mixing index and pressure drop were evaluated and co...

in this paper, a neural network model reference adaptive system speed observer is designed, which can be used in speed control of linear induction motors (lims). dynamical equations of lim have been considered accurate. in other words, the end effect and the electrical losses of the motor have been included in the motor equivalent circuit. then equations of the reference model and adaptive mode...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

we introduce a new solution for kawahara-kdv equations. the lie group analysis is used to carry out the integration of this equations. the similarity reductions and exact solutions are obtained based on the optimal system method.

in recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. these two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. in this paper i will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.