Firas Kaabi

collaborators

5 papers

math.AP2026

Sharp Lifespan Estimates for a Semilinear Wave Equation with Nonlinear Damping

Firas Kaabi

We study the maximal existence time $T^{*} (ϱ)$ of the solution of the semilinear wave equation $u_{tt} - Δ u = u ∣ u ∣^{p - 1} - u_{t} ∣ u_{t} ∣^{q - 1}$ in a bounded domain, with Dirichlet b…

math.AP2026

Small-Data Lifespan for a One-Dimensional Wave Equation with Mixed Characteristic-Time Derivative Source

Firas Kaabi

We study the lifespan of classical solutions to \[ v_{tt}-v_{xx}=|v_t+v_x|^m|v_t|^n, \qquad x\in\R,\quad t>0, \] where $m>1$ and $n>1$. For compactly supported data $(ηϕ,ηψ)$…

math.AP2026

Two-sided estimates of the blow-up time for a semilinear wave equation with fractional structural damping

Firas Kaabi

We consider the initial--boundary value problem for the semilinear wave equation with fractional structural damping $u_{tt} + (- Δ)^{θ} u_{t} - Δ u = ∣ u ∣^{p - 1} u$ in a bounded domain, wher…

math.AP2026

Lifespan Lower Estimates for a Strongly Damped Semilinear Wave Equation

Firas Kaabi

We consider a strongly damped semilinear wave equation with initial data prescribed as $(ϱϕ, ϱ h)$ , where the profiles are fixed and only the amplitude $ϱ > 0$ is al…

math.AP2026

Regularity and singularity of the blow-up curve for a wave equation with a derivative nonlinearity and a scale-invariant damping

Ahmed Bchatnia, Makram Hamouda, Firas Kaabi +2

In this article, we investigate the blow-up behavior of solutions to the one-dimensional damped nonlinear wave equation, namely $$ \partial_t^2 u - \partial_x^2 u + \fracμ{1 + t} \…