Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
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QDD137 - 10/30/2012
Grillo, G.; Kovarik, H.
Weighted dispersive estimates for two-dimensional Schroedinger operators with Aharonov-Bohm magnetic field | Abstract | | We consider two-dimensional Schroedinger operators with Aharonov-Bohm magnetic field and an additional electric potential.
We obtain an explicit leading term of the asymptotic expansion of the unitary group associated to H for large times in weighted L^2 spaces. In particular, we show that the magnetic field improves the decay of the unitary group with respect to the unitary group generated by non-magnetic Schroedinger operators, and that the decay rate in time is determined by the magnetic flux. |
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QDD135 - 10/29/2012
Bertacchi, D.; Zucca, F.
Strong local survival of branching random walks is not monotone | Abstract | | The aim of this paper is the study of the strong local survival property for discrete-time and continuous-time branching random walks. We study this property by means of an infinite dimensional generating function G and a maximum principle which, we prove, is satisfied by every fixed point of G.
We give results about the existence of a strong local survival regime and we prove that, unlike local and global survival, in continuous time, strong local survival is not a monotone property in the general case (though it is monotone if the branching random walk is quasi transitive).
We provide an example of an irreducible branching random walk
where the strong local property depends on the starting site of the process.
By means of other counterexamples we show that the existence of a pure global phase is not equivalent to nonamenability of the process, and that even a branching random walk with the same branching law at each site may not exhibit strong local survival.
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QDD136 - 10/29/2012
Zucca, F.
Persistent and susceptible bacteria with individual deaths | Abstract | | The aim of this paper is to study two models for a bacterial population subject to antibiotic treatments.
It is known that some bacteria are sensitive to antibiotics. These bacteria are in a state called persistence and each bacterium can switch from this state to a non-persistent (or susceptible) state and back.
Our models extend those introduced in [6] by adding a (random) natural life cycle for each bacterium and
by allowing bacteria in the susceptible state to escape
the action of the antibiotics with a fixed probability
1-p (while every bacterium in a persistent state survives with
probability 1). In the first model we inject the antibiotics in the system at fixed, deterministic times while in the second one the time intervals are random.
We show that, in order to kill eventually the whole bacterial population, these time intervals cannot be too large . The maximum admissible length is increasing with respect to
p and it decreases rapidly when p<1.
While in the case p=1 switching back and forth to the persistent state is the only chance of surviving
for bacteria, when p<1 and the death rate in the persistent case is positive then switching state is not always a good strategy from the bacteria point of view.
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QDD133 - 10/04/2012
Grillo, G.; Muratori, M.; Punzo, F.
Conditions at infinity for the inhomogeneous filtration equation | Abstract | | We investigate existence and uniqueness of solutions to the
filtration equation with an inhomogeneous density in ${ mathbb R}^N$, approaching at infinity a given continuous datum of Dirichlet type. |
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QDD134 - 10/04/2012
Grillo, G.; Muratori, M.
Sharp short and long time L^ infty bounds for solutions to porous media equations with homogeneous Neumann boundary conditions | Abstract | | We study a class of nonlinear diffusion equations whose model is the classical porous media equation on euclidean domains, with homogeneous Neumann boundary conditions. We improve the known results in such model case, proving sharp uniform regularizing properties of the evolution for short time and sharp long time bounds for convergence of solutions to their mean value. The generality of the discussion allows to consider, almost at the same time, weighted versions of the above equation provided an appropriate weighted Sobolev inequality holds. In fact, we show that the validity of such weighted Sobolev inequality is equivalent to the validity of a suitable regularizing bound for solutions to the associated weighted porous media equation.
The long time asymptotic analysis relies on the assumed weighted Sobolev inequality only, and allows to prove uniform convergence to the mean value, with the rate predicted by linearization, in such generality. |
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QDD130 - 10/02/2012
Barbatis, G; Gazzola, F.
Higher order linear parabolic equations | Abstract | | We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the updated state of art and we suggest several open problems. |
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QDD131 - 10/02/2012
Bramanti, M.; Cupini, G.; Lanconelli, E.; Priola, E.
Global L^{p} estimates for degenerate Ornstein Uhlenbeck operators with variable coefficients | Abstract | | We consider a class of degenerate Ornstein-Uhlenbeck operators A in R^N, where A is the sum of a principal part in
nondivergence form, with uniformly continuous and bounded entries, which is uniformly elliptic on R^s (s
( drift ) which is linear in x and such that if we freeze the principal part at any point x_0 we get a hypoelliptic operator. For this class of operators we prove global L^p estimates (1
the previous estimates as a byproduct of analogous estimates for the corresponding evolution operator of Kolmogorov-Fokker-Planck type,
A-D_t, on a strip R^N x[-T,T], when the coefficients of the principal part depend on (x,t).
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QDD132 - 10/02/2012
Bramanti, M.; Fanciullo, M. S.
BMO estimates for nonvariational operators with discontinuous coefficients structured on Hörmander s vector fields on Carnot groups | Abstract | | We consider a class of nonvariational linear operators formed by homogeneous left invariant Hormander s vector fields with respect to a structure of Carnot group. The bounded coefficients of the operators belong to the vanishing logarithmic mean oscillation class with respect to the distance induced by the vector fields (in particular they can be discontinuous). We prove local estimates in local BMO spaces intersected with the Lebesgue spaces. Even in the uniformly elliptic case our estimates improve the known results. |
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