152 citations · 547 across the 17 of their papers we have counts for
19 papers
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),…
The critical exponent for semilinear wave equations with damped oscillations
Marcello D'Abbicco
We determine the existence exponent for the global small data solutions for a class of evolution equations with power nonlinearity under the effect of a dissipation that dampen the…
A class of multipliers from to the Hardy space
Marcello D'Abbicco
In this note, we show a condition on the derivatives of a multiplier that guarantees that is a multiplier from to the Hardy Space $H^1(\math…
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…
Semilinear damped wave equations with data from Sobolev spaces of negative order: the critical case in Euclidean setting and in the Heisenberg space
Marcello D'Abbicco
In this note, we prove the global existence of solutions to the semilinear damped wave equation in , , with critical nonlinearity under the assumption that th…
Sharp Lp-Lq estimates for evolution equations with damped oscillations
Marcello D'Abbicco, Marcelo Rempel Ebert
In this paper we derive sharp estimates, (including endpoint estimates as and ) for dissipative wave-type equations, un…
Asymptotics of higher order hyperbolic equations with one or two dissipative lower order terms
Marcello D'Abbicco
In this paper, we consider the Cauchy problem for a hyperbolic equation of any order , where and , and $Q=P_m+P_{m-…
Asymptotic profiles for a wave equation with parameter dependent logarithmic damping
Ruy Coimbra Charao, Marcello D'Abbicco, Ryo Ikehata
We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the C…
The semilinear Euler-Poisson-Darboux equation: a case of wave with critical dissipation
Marcello D'Abbicco
In this paper we study the existence of global-in-time energy solutions to the Cauchy problem for the Euler-Poisson-Darboux equation, with a power nonlinearity: $$u_{tt}-u_{xx} + \…
A test function method for evolution equations with fractional powers of the Laplace operator
Kazumasa Fujiwara, Marcello D'Abbicco
In this paper, we discuss a test function method to obtain nonexistence of global-in-time solutions for higher order evolution equations with fractional derivatives and a power non…
The critical exponent for nonlinear damped -evolution equations
Marcello D'Abbicco, Marcelo Rempel Ebert
In this paper, we derive suitable optimal decay estimates, , for the solutions to the -evolution equation, , with structural damping and…
The critical exponent(s) for the semilinear fractional diffusive equation
Marcello D'Abbicco, Marcelo Rempel Ebert, Tiago Henrique Picon
In this paper we show that there exist two different critical exponents for global small data solutions to the semilinear fractional diffusive equation with Caputo fractional deriv…
Weak stability of the plasma-vacuum interface problem
Davide Catania, Marcello D'Abbicco, Paolo Secchi
We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed b…
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Marcello D'Abbicco, Sandra Lucente, Michael Reissig
In this note we study the global existence of small data solutions to the Cauchy problem for the semi-linear wave equation with a not effective scale-invariant damping term, namely…
Stability of the linearized MHD-Maxwell free interface problem
Davide Catania, Marcello D'Abbicco, Paolo Secchi
We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual comp…
The Threshold between Effective and Noneffective Damping for Semilinear Waves
Marcello D'Abbicco
In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the…
A modified test function method for damped waves
Marcello D'Abbicco, Sandra Lucente
In this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical ex…
Semi-linear structural damped waves
Marcello D'Abbicco, Michael Reissig
We study the global existence of small data solutions for Cauchy problem for the semi-linear structural damped wave equation with source term.
Semi-linear wave equations with effective damping
Marcello D'Abbicco, Sandra Lucente, Michael Reissig
We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existe…