Author

Firas Kaabi

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Preprint Sep 2026

Sharp Lifespan Estimates for a Semilinear Wave Equation with Nonlinear Damping

We study the maximal existence time $T^{*}(\varrho)$ of the solution of the semilinear wave equation $u_{tt}-\Delta u=u|u|^{p-1}-u_{t}|u_{t}|^{q-1}$ in a bounded domain, with Dirichlet boundary condition and initial data $(\varrho f,\varrho g)$, where $1<q<p$ and the amplitude $\varrho$ is large. For nontrivial $f$ and...

Firas Kaabi · 0 citations

Preprint Aug 2026

Characteristic localization, sharp lifespan asymptotics and global dynamics for a one-dimensional derivative wave equation

We study the Cauchy problem $$ v_{tt}-v_{xx}=\abs{v_t+v_x}^{m}\abs{v_t}^{n}, \qquad v(x,0)=\eta\varphi(x),\quad v_t(x,0)=\eta\psi(x), $$ on $\R$, with compactly supported profiles $\varphi\in C_0^2(\R)$, $\psi\in C_0^1(\R)$, exponents $m,n>1$, and amplitude $\eta>0$. We show that the sign of $P_0=\psi+\varphi'$ decides...

Firas Kaabi · 0 citations