Mama Abdelli

• Doctor at Mascara University, Algeria

We consider a locally nonlinear damped plate equation in a bounded domain where the damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo-Galerkin method, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the localization of the damping, w...

In this paper, we consider the initial-boundary value problem for a class of nonlinear coupled wave equation and Petrovesky system in a bounded domain. The strong damping is nonlinear. First, we prove the existence of global weak solutions by using the energy method combined with Faedo-Galarkin method and the multiplier method. In addition, under s...

We consider the wave equation with a locally damping and a nonlinear source term in a bounded domain. y tt − ∆y + a(x)g(y t) = |y| p−2 y, where p > 2. The damping is nonlinear and is effective only in a neighborhood of a suitable subset of the boundary. We show, for certain initial data and suitable conditions on g, a and p that this solution is gl...

The aim of this research study is to investigate the viscoelastic Petrovsky equation with nonlinear frictional damping and a relaxation function g. Using Faedo-Galerkin's procedure, we establish the existence of the solution. Furthermore, we prove explicit and general decay rate results by using the multiplier method and some properties of the conv...

We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t\rightarrow...

In this paper, we consider an Euler–Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary conditions are satisfied. We prove the existence and uniqueness of global solution under suitable assumptions on the tension of beam and on the parameters of the problem....

In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*} We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with...

In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving non-constant velocity and dynamical boundary conditions are satisfied. By using a semigroup approach, we prove the existence and uniqueness of global solution under suitable assumptions on the tension of beam and on the p...

This paper is devoted to prove the pointwise controllability of the Euler–Bernoulli beam equation. It is obtained as a limit of internal controllability of the same type of equation. Our approach is based on the techniques used in Fabre and Puel (Port Math 51:335–350, 1994).

We consider the scalar second order ODE u + |u | $\alpha$ u + |u| $\beta$ u = 0, where $\alpha$, $\beta$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 < $\alpha$ < $\beta$ and moreover there is a constant C independent of the initial...

In this article we consider a nonlinear viscoelastic Petrovsky equation in a bounded domain with distributed delay |ut (x, t)|lutt (x, t) + �2u(x, t) − �utt (x, t) − � t 0 h(t − σ)�2u(x, σ) dσ + μ1ut (x, t) + � τ2 τ1 μ2(s)ut (x, t − s)ds = 0, x ∈ �, t > 0, and prove a global solution existence result using the energy method combined with the Faedo–...

In this article we consider a nonlinear viscoelastic Petrovsky equation in a bounded domain with a delay term in the weakly nonlinear internal feedback: (Formula Presented). We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay...

The initial value problem and global properties of solutions are studied for the vector equation: $\left(\left\Vert u'\right\Vert ^ l u'\right)' + \left\Vert A^{\frac{1}{2}} u \right\Vert^\beta A u + g(u ') = 0$ in a finite dimensional Hilbert space under suitable assumptions on g.

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This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.

In this paper the initial value problem and global properties of solutions are studied for the scalar second order ODE: (vertical bar u'vertical bar(l)u')' + c vertical bar u'vertical bar(alpha)u' + d vertical bar u vertical bar(beta)u = 0, where alpha, beta, l, c, d are positive constants. In particular, existence, uniqueness and regularity as wel...

In this paper we study decay properties of the solutions to the degenerate Kirchhoff equation with a weak nonlinear dissipative term.