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math.AP2026
On the two critical exponents for a dispersive equation with weak dissipation
Marcello D'Abbicco, Antonio Lagioia
In this paper, we study a nonlinear Cauchy problem written in normal form \begin{equation*} \begin{cases} u_{tt} + A u+ Bu_t =D|u|^α, & t\geq 0, x \in \mathbb{R}^n\\ u(0,x)=u_0(x),…
math.AP2026
Dispersive-Dissipative estimates for Boussinesq and other generalized wave equations
Marcello D'Abbicco, Marcelo Rempel Ebert, Antonio Lagioia
We derive dispersive-dissipative estimates for multipliers associated to a general class of wave-type equations, in particular for the viscous Boussinesq equation. The dispersion i…
math.AP2024
estimates for solutions to the plate equation with mass term
Alexandre Arias Junior, Halit Sevki Aslan, Antonio Lagioia +1
In this paper, we study the Cauchy problem for the linear plate equation with mass term and its applications to semilinear models. For the linear problem we obtain estima…