Zobrazeno 1 - 10
of 111
pro vyhledávání: '"D'Abbicco, Marcello"'
Autor:
D'Abbicco, Marcello
In this note, we prove the global existence of solutions to the semilinear damped wave equation in $\mathbb{R}^n$, $n\leq6$, with critical nonlinearity under the assumption that the initial data are small in the energy space $H^1\times L^2$ and under
Externí odkaz:
http://arxiv.org/abs/2408.11756
In this paper we derive $L^p-L^q$ estimates, with $1\leq p\leq q\leq\infty$ (including endpoint estimates as $L^1-L^1$ and $L^1-L^\infty$), for the solution to \[ \begin{cases} u_{tt}-\Delta u + Au_t =0, \quad t\in\mathbb{R}_+,\, x\in \mathbb{R}^n, \
Externí odkaz:
http://arxiv.org/abs/2311.03173
Autor:
D'Abbicco, Marcello
In this paper, we consider the Cauchy problem for a hyperbolic equation $Q(\partial_t,\partial_x)u=0$ of any order $m\geq3$, where $t\geq0$ and $x\in\mathbb{R}^n$, and $Q=P_m+P_{m-1}+P_{m-2}$ is a sum of homogeneous hyperbolic polynomials $P_{m-j}$ o
Externí odkaz:
http://arxiv.org/abs/2109.14067
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 Cauchy problem for this model in the whole space and we study the asymp
Externí odkaz:
http://arxiv.org/abs/2009.06395
Autor:
D'Abbicco, Marcello
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: $$u_{tt}-u_{xx} + \frac\mu{t}\,u_t = |u|^p \,, \quad t>t_0, \ x\in\mathbb{R}\,.$$ Here ei
Externí odkaz:
http://arxiv.org/abs/2008.08703
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 nonlinearity, under a sign condition on the initial data. In order to dea
Externí odkaz:
http://arxiv.org/abs/2005.12056
In this paper, we derive suitable optimal $L^p-L^q$ decay estimates, $1\leq p\leq q\leq \infty$, for the solutions to the $\sigma$-evolution equation, $\sigma>1$, with structural damping and power nonlinearity $|u|^{1+\alpha}$ or $|u_t|^{1+\alpha}$,
Externí odkaz:
http://arxiv.org/abs/2005.10946
Publikováno v:
J Fourier Anal Appl (2018)
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 derivative in time. The second critical exponent appears if the second data
Externí odkaz:
http://arxiv.org/abs/1709.03285
Autor:
D'Abbicco, Marcello, Girardi, Giovanni
Publikováno v:
Mathematical Methods in the Applied Sciences; 9/15/2024, Vol. 47 Issue 13, p10872-10890, 19p
