Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica.
La presenza del full-text è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 866 prodotti
-
QDD159 - 15/07/2013
Noris, B.; Tavares, H.; Verzini, G.
Existence and orbital stability of the ground states with prescribed mass for the L^2-critical 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^2-critical and subcritical, while they are almost always stable in the L^2-supercritical 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 Landesman-Lazer 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 Galton-Watson 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 1-dimensional 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 Galton-Watson 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 in finite 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 two-step 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 fi rst 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 drug-resistance 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. |
-
QDD153 - 03/04/2013
Grillo, G.; Muratori, M.
Sharp asymptotics for the porous media equation in low dimensions via Gagliardo-Nirenberg inequalities | Abstract | | We prove sharp asymptotic bounds for solutions to the porous media equation with homogeneous Dirichlet or Neumann boundary conditions on a bounded Euclidean domain, in dimension one and two. This is achieved by making use of appropriate Gagliardo-Nirenberg inequalities only. The generality of the discussion allows to prove similar bounds for weighted porous media equations, provided one deals with weights for which suitable Gagliardo-Nirenberg inequalities hold true. Moreover, we show equivalence between such functional inequalities and the mentioned asymptotic bounds for solutions. |
|
