In this work, the dynamic response of Euler–Bernoulli beams four different boundary conditions with fractional order internal damping under a traversing moving load is investigated. The assumed to be values constant velocity. A proposed approach obtain closed-form solution problem based on Green’s functions combined decomposition technique in Laplace transform domain introduced. Several cases a...

We proved global existence and uniqueness of classical solutions to the initial boundary value problem for the 3D damped compressible Euler equations on bounded domain with slip boundary condition when the initial data is near its equilibrium. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy’s law. Based on energ...

We construct global L∞ entropy weak solutions to the initial boundary value problem for the damped compressible Euler equations on bounded domain with physical boundaries. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy’s law. Based on entropy principle, we showed that the physical weak solutions converges to st...

We study in this paper the stability of a system type Rao–Nakra sandwich beam whole line $\mathbb{R}$ under linear frictional dampings acting on two wave equations. prove that $L^2(\mathbb{R})$-norm solutions and their higher order derivatives with respect to space variable converge polynomially zero as time goes infinity. These decay estimates are obtained independently parameters spite fact E...

We present an extension of some results higher order calculus variations and optimal control to generalized functions. The framework is the category smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary prove Euler–Lagrange equations, D’Alembert principle in differential form, du Bois–Reymond optimality condition Noether’s theorem. start ...

In this paper we study the linearized Vlasov--Poisson equation for localized disturbances of an infinite, homogeneous Maxwellian background distribution in $\mathbb{R}^3_x \times \mathbb{R}^3_v$. contrast to confined case $\mathbb{T}^d_x \mathbb{R}_v^d$, or unconfined $\mathbb{R}^d_x \mathbb{R}^d_v$ with screening, dynamics disturbance are not scattering towards free transport as $t \to \pm \in...

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...