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math.AP2026
Dispersive estimates for wave-type equations with time-dependent damping
Halit Sevki Aslan, Marcelo Rempel Ebert
In this paper, we study the Cauchy problem for a class of semilinear evolution equations with scale-invariant time-dependent dissipation \begin{equation*} \begin{cases} u_{tt} + L_…
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.AP2019
The influence of data regularity in the critical exponent for a class of semilinear evolutions equations
Marcelo R. Ebert, Cleverson R. Da Luz, MaÍra F. G. Palma
In this paper we find the critical exponent for the global existence (in time) of small data solutions to the Cauchy problem for the semilinear dissipative evolution equations % \[…