arXiv subjects

Mohammad Kafini

Publications and source records attributed to Mohammad Kafini.

4 recordsLinked to original sources

arXiv2026

On the wave equation with logarithmic damping: wellposedness, blow-up and numerical analysis

In this work, we are concern with the wave equation subjected to a nonlinear feedback of logarithmic type and nonlinear polynomial source. To achieve a comprehensive understanding of this novel damping mechanism, we start with studying the well-posedness and the uniqueness of the problem. Then we establish the blow-up result of the problem under suitable initial data with negative initial energy and critical exponent of the source term. Finally, we present a brief numerical study and examples that support our result.

math.AP↗

arXiv2024

On the wave equation with variable exponent nonlinearity and distributive delay

In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be dominated. Secondly, global existence of solutions is shown under some suitable conditions on the initial data. Finally, the decay rates of that solutions are established as well.

math.AP↗

arXiv2024

Blow-up result for a piezoelectric beams system with magnetic effects

The system under studying is for a piezoelectric beams system with magnetic effects, frictional dampings and source terms. We use the concavity method to study the competition of the dampings and the sources that leads to a blow-up result for solutions with negative initial energy.

math.AP↗

arXiv2021

Stability result for a viscoelastic wave equation in the presence of finite and infinite memories

In this paper, we are concerned with the following viscoelastic wave equation \begin{equation*} \label{1} u_{tt}-\nabla u +\int_0^t g_1 (t-s)~ div(a_1(x) \nabla u(s))~ ds + \int_0^{+ \infty} g_2 (s)~ div(a_2(x) \nabla u(t-s)) ~ds = 0, \end{equation*} in a bounded domain $Ω$. Under suitable conditions on $a_1$ and $a_2$ and for a wide class of relaxation functions $g_1$ and $g_2$. We establish a general decay result. The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data $\nabla u_{0}$. This study generalizes and improves previous literature outcomes.

math.AP↗