Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica. La presenza del fulltext è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 867 prodotti

QDD160  29/07/2013
Ferrero, A.; Gazzola, F.
A partially hinged rectangular plate as a model for suspension bridges  Abstract   A plate model describing the statics and dynamics of a suspension bridge is suggested. A partially hinged plate subject to nonlinear restoring hangers is considered. The whole theory from linear problems, through nonlinear stationary equations, ending with the full hyperbolic evolution equation is studied. This paper aims to be the starting point for more refined models. 

QDD159  15/07/2013
Noris, B.; Tavares, H.; Verzini, G.
Existence and orbital stability of the ground states with prescribed mass for the L^2critical and supercritical NLS on bounded domains  Abstract   We study solutions of a semilinear elliptic equation with prescribed mass and Dirichlet homogeneous boundary conditions in the unitary ball. Such problem arises in the search of solitary wave solutions for nonlinear Schrödinger equations (NLS) with Sobolev subcritical power nonlinearity on bounded domains. Necessary and sufficient conditions are provided for the existence of such solutions. Moreover, we show that standing waves associated to least energy solutions are always orbitally stable when the nonlinearity is L^2critical and subcritical, while they are almost always stable in the L^2supercritical regime. The proofs are obtained in connection with the study of a variational problem with two constraints, of independent interest: to maximize the L^{p+1}norm among functions having prescribed L^2 and H^1_0 norm. 

QDD158  07/06/2013
Soave, N.; Verzini, G.
Bounded solutions for a forced bounded oscillator without friction  Abstract   Under the validity of a LandesmanLazer type condition, we prove the existence of solutions bounded on the real line, together with their first derivatives, for some second order nonlinear differential equation of the form ü + g(u) = p(t), where the reaction term g is bounded. The proof is variational, and relies on a dual version of the Nehari method for the existence of oscillating solutions to superlinear equations. 

QDD156  31/05/2013
BERTACCHI, D.; ZUCCA, F.
Rumor processes in random environment on N and on GaltonWatson trees  Abstract   The aim of this paper is to study rumor processes in random environment. In a rumor
process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from
vertex to vertex. We consider two rumor processes. In the rework process each station, when
reached by the signal, transmits it up to a random distance. In the reverse rework process, on the
other hand, stations do not send any signal but they listen for it up to a random distance. The
first random environment that we consider is the deterministic 1dimensional tree N with a random
number of stations on each vertex; in this case the root is the origin of N. We give conditions for
the survival/extinction on almost every realization of the sequence of stations. Later on, we study
the processes on GaltonWatson trees with random number of stations on each vertex. We show
that if the probability of survival is positive, then there is survival on almost every realization of
the infinite tree such that there is at least one station at the root. We characterize the survival of
the process in some cases and we give sufficient conditions for survival/extinction. 

QDD157  31/05/2013
BERTACCHI, D.; ZUCCA, F.; FORESTI, S.; MANGIONI, D.; GORI, A.
COMBINATION VERSUS SEQUENTIAL MONOTHERAPY IN CHRONIC HBV INFECTION: A MATHEMATICAL APPROACH  Abstract   Sequential monotherapy is the most widely used therapeutic approach in the treatment
of HBV chronic infection. Unfortunately, under therapy, in some patients the hepatitis virus mutates
and gives rise to variants which are drug resistant. We conjecture that combination therapy is able
to delay drug resistance for a longer time than sequential monotherapy. To study the action of
these two therapeutic approaches in the event of unknown mutations and to explain the emergence
of drug resistance, we propose a stochastic model for the infection within a patient which is treated
with two drugs, either sequentially or contemporaneously, and develops a twostep mutation which
is resistant to both drugs. We study the deterministic approximation of our stochastic model and
give a biological interpretation of its asymptotic behaviour. We compare the time when this new
strain first reaches detectability in the serum viral load. Our results show that the best choice is
to start an early combination therapy, which allows to stay drugresistance free for a longer time. 

QDD155  16/05/2013
Bramanti, M.; Brandolini, L.; Manfredini, M.; Pedroni, M.
Fundamental solutions and local solvability for nonsmooth Hörmander s operators  Abstract   We consider operators of the form $L= sum_{i=1}^{n}X_{i}^{2}+X_{0}$ in a bounded domain of R^p where X_0, X_1,...,X_n are nonsmooth Hörmander s vector fields of step r such that the highest order commutators are only Hölder continuous. Applying Levi s parametrix method we construct a local fundamental solution gamma for L and provide growth estimates for gamma and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients we prove that gamma also possesses second derivatives, and we deduce the local solvability of L, constructing, by means of gamma, a solution to Lu=f with H older continuous f. We also prove $C_{X,loc}^{2, alpha}$ estimates on this solution. 

QDD154  18/04/2013
Bramanti, M.; Fanciullo, M. S.
C^{k,alpha}regularity of solutions to quasilinear equations structured on Hoermander's vector fields  Abstract   For a linear nonvariational operator structured on smooth
Hörmander s vector fields, with Hölder continuous coefficients, we prove a regularity result in the spaces of Hölder functions. We deduce an analogous regularity result for nonvariational degenerate quasilinear equations. 

QDD152  03/04/2013
Grillo, G.; Muratori, M.
Radial fast diffusion on the hyperbolic space  Abstract   We consider positive radial solutions to the fast diffusion equation on the hyperbolic space. By radial we mean solutions depending only on the geodesic distance from a given point. We investigate the fine asymptotics of solutions near the extinction time, in terms of a separable solution, showing convergence in relative error of the former to the latter. Solutions are smooth, and bounds on derivatives are given as well. In particular, sharp convergence results are shown for spatial derivatives, again in the form of convergence in relative error. 
