Abstract:
A three-phase pesticide transport model is used to verify by numerical simulation, the influence of different parameters on infiltration through soil and/or surface runoff processes. Simulations are performed for a typical sandy loam potato field of Italy’s Fucino Plain, to explain the occurrence of measured concentrations of pesticides (mainly Linuron) in both surface waters and groundwater. Simulations take into account agricultural practices, climatic conditions, and soil characteristics. Results focus on the role of rainfall events and irrigation, of related infiltration amount and distribution, and of root zone thickness in influencing pesticide fate and its possible concentration increase through the years. Modeling results positively fit with the background knowledge of the Plain hydrology, showing the prevalence of surface transport and a scarce possibility for pesticides to reach groundwater in an average rainfall/irrigation scenario. Meanwhile, specific water management strategies are suggested to limit the occurrence of local groundwater pollution, related to high aquifer vulnerability zones, controlling inappropriate irrigation and pesticide application.

Abstract:
Let $Omegasubseteq mathbb{R}^N$ a bounded open set, $Ngeq 2$, and let $p>1$; in this paper we study the asymptotic behavior with respect to the time variable $t$ of the entropy solution of nonlinear parabolic problems whose model is $$displaylines{ u_{t}(x,t)-Delta_{p} u(x,t)=mu quad hbox{in } Omega imes(0,infty),cr u(x,0)=u_{0}(x) quad hbox{in } Omega, }$$ where $u_0 in L^{1}(Omega)$, and $muin mathcal{M}_{0}(Q)$ is a measure with bounded variation over $Q=Omega imes(0,infty)$ which does not charge the sets of zero $p$-capacity; moreover we consider $mu$ that does not depend on time. In particular, we prove that solutions of such problems converge to stationary solutions.

Abstract:
We deal with existence, uniqueness, and regularity for solutions of the boundary value problem $$ \begin{cases} {\mathcal L}^s u = \mu &\quad \text{in $\Omega$},\newline u(x)=0 \quad &\text{on} \ \ \mathbb{R}^N\backslash\Omega, \end{cases} $$ where $\Omega$ is a bounded domain of $\mathbb{R}^N$, $\mu$ is a bounded radon measure on $\Omega$, and ${\mathcal L}^s$ is a nonlocal operator of fractional order $s$ whose kernel $K$ is comparable with the one of the factional laplacian.

Abstract:
In this paper we prove a nonexistence result for nonlinear parabolic problems with zero lower order term whose model is $$ \begin{cases} u_{t}- \Delta_p u+|u|^{q-1}u=\lambda & \text{in}\ (0,T)\times\Omega u(0,x)=0 & \text{in}\ \Omega,\\ u(t,x)=0 & \text{on}\ (0,T)\times\partial\Omega, \end{cases} $$ where $\Delta_p ={\rm div }(|\nabla u|^{p-2}\nabla u)$ is the usual $p$-laplace operator, $\lambda$ is measure concentrated on a set of zero parabolic $r$-capacity ($1

Abstract:
In this paper we study existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is $$ \begin{cases} -\sum_{m=1}^{\infty} a_m \Delta u^m= f&\text{in}\ \Omega \newline u=0 & \text{on}\ \partial\Omega\,, \end{cases} $$ where $\Omega$ is a bounded domain of $\mathbb{R}^N$, $a_m$ is a sequence of nonnegative real numbers, and $f$ is in $L^q(\Omega)$, $q>\frac{N}{2}$.

Abstract:
In this paper we deal with the asymptotic behavior as $t$ tends to infinity of solutions for linear parabolic equations whose model is $$ \begin{cases} u_{t}-\Delta u = \mu & \text{in}\ (0,T)\times\Omega,\\[0.7 ex] u(0,x)=u_0 & \text{in}\ \Omega, \end{cases} $$ where $\mu$ is a general, possibly singular, Radon measure which does not depend on time, and $u_0\in L^{1}(\Omega)$. We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by G. Stampacchia) of the associated elliptic problem.

Abstract:
Let $\Omega\subseteq \mathbb{R}^N$ a bounded open set, $N\geq 2$, and let $p>1$; we prove existence of a renormalized solution for parabolic problems whose model is $$ \begin{cases} u_{t}-\Delta_{p} u=\mu & \text{in}\ (0,T)\times\Omega,\newline u(0,x)=u_0 & \text{in}\ \Omega,\newline u(t,x)=0 &\text{on}\ (0,T)\times\partial\Omega, \end{cases} $$ where $T>0$ is any positive constant, $\mu\in M(Q)$ is a any measure with bounded variation over $Q=(0,T)\times\Omega$, and $u_o\in L^1(\Omega)$, and $-\Delta_{p} u=-{\rm div} (|\nabla u|^{p-2}\nabla u )$ is the usual $p$-laplacian.

Abstract:
We review the plasma phenomenology in the astrophysical sources which show appreciable radio emissions, namely Radio-Jets from Pulsars, Microquasars, Quasars and Radio-Active Galaxies. A description of their basic features is presented, then we discuss in some details the links between their morphology and the mechanisms that lead to the different radio-emissions, investigating especially the role played by the plasma configurations surrounding compact objects (Neutron Stars, Black Holes). For the sake of completeness, we briefly mention observational techniques and detectors, whose structure set them apart from other astrophysical instruments. The fundamental ideas concerning Angular Momentum Transport across plasma accretion disks (together with the disk-source-jet coupling problem) are discussed, by stressing their successes and their shortcomings. An alternative scenario is then inferred, based on a parallelism between astrophysical and laboratory plasma configurations, where small-scale structures can be found. We will focus our attention on the morphology of the radio-jets, on their coupling with the accretion disks and on the possible triggering phenomena, viewed as profiles of plasma instabilities.

Abstract:
We examine the morphology of magnetic structures in thin plasma accretion discs, generalizing a stationary ideal MHD model to the time-dependent visco-resistive case. Our analysis deals with small scale perturbations to a central dipole-like magnetic field, which give rise -- as in the ideal case -- to the periodic modulation of magnetic flux surfaces along the radial direction, corresponding to the formation of a toroidal current channels sequence. These microstructures suffer an exponential damping in time because of the non-zero resistivity coefficient, allowing us to define a configuration lifetime which mainly depends on the midplane temperature and on the length scale of the structure itself. By means of this lifetime we show that the microstructures can exist within the inner region of stellar discs in a precise range of temperatures, and that their duration is consistent with local transient processes (minutes to hours).

Abstract:
In this paper we deal with local estimates for parabolic problems in $\mathbb{R}^N$ with absorbing first order terms, whose model is $\{ {l} u_t- \Delta u +u |\nabla u|^q = f(t,x) \quad &{in}\, (0,T) \times \mathbb{R}^N\,, \\[1.5 ex] u(0,x)= u_0 (x) &box{in}\, \mathbb{R}^N.$ where $T>0$, $N\geq 2$, $1