5 papers
Sharp Lifespan Estimates for a Semilinear Wave Equation with Nonlinear Damping
Firas Kaabi
We study the maximal existence time of the solution of the semilinear wave equation in a bounded domain, with Dirichlet b…
Characteristic localization, sharp lifespan asymptotics and global dynamics for a one-dimensional derivative wave equation
Firas Kaabi
We study the Cauchy problem $$ v_{tt}-v_{xx}=\abs{v_t+v_x}^{m}\abs{v_t}^{n}, \qquad v(x,0)=ηφ(x),\quad v_t(x,0)=ηψ(x), $$ on , with compactly supported profiles $φ\in C_0^2(\R)…
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 in a bounded domain, wher…
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 , where the profiles are fixed and only the amplitude is al…
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} \…