891 research outputs found
Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
No full textIn this paper we prove a comparison result between viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form u_t+H(x,Du)=0 in R^Nx(0,T) where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation
Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
No full textIn this paper we prove comparison
principles between viscosity semicontinuous sub- and
supersolutions of the generalized Dirichlet problem (in the sense
of viscosity solutions) for the {\it Levi Monge-Amp\`{e}re}
equation. As a consequence of this result and of the Perron's
method we get the existence of a continuous solution of the
Dirichlet problem related to the prescribed Levi curvature
equation under suitable assumptions on the boundary data and on
the Levi curvature of the domain. We also show that such a
solution is Lipschitz continuous by building Lipschitz continuous
barriers and by applying a weak Bernstein method
Large time behavior of solutions to parabolic equations with Neumann boundary conditions
No full textAbstractIn this paper we are interested in the large time behavior as t→+∞ of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521–541]
Propagation of maxima and strong maximum principle for fully nonlinear degenerate elliptic equations. Part I: convex operators
No full textPropagation of maxima and strong maximum principle for fully nonlinear degenerate elliptic equations. Part II: concave operators
No full textBio-geomorphic patterns in tidal environments
No full textIn times of natural and anthropogenic climate change, tidal bio-geomorphic systems are most exposed to possibly irreversible transformations with far-reaching ecological and
socio-economic implications.
It is thus of critical importance to develop models for predicting the evolution of such systems under varying forcings and, if
present, their dynamically-accessible stable states.
The notion that freshwater and terrestrial ecosystems may switch
abruptly to alternative stable states as a result of feedbacks
between consumers and limiting resources is widely acknowledged. On the contrary, theoretical or observational proofs of the existence of alternative equilibrium states in intertidal ecosystems has until recently proven to be elusive.
This is due to a prevalent reductionist approach, which has until recently mostly produced either purely ecological or purely geomorphological models, while the coupled dynamics of landforms and biota in the intertidal zone has remained largely unexplored.
The presence and continued existence of tidal morphologies, and in particular of salt marshes, is intimately connected with biological activity, especially with the presence of halophytic vegetation. In fact, observations and models coupling geomorphological and biological processes indicate that vegetation crucially affects marsh equilibrium configurations through the production of organic soil, the capture of sediment, and the stabilization against erosion produced by wind waves. Often, different vegetation species live within very narrow
elevation intervals, associated with similarly narrow ranges of environmental pressures, thus leading to the emerge of the zonation phenomenon.
Here we present modeling analysis on the spatial distribution of geomorphological and vegetational spatial patterns in tidal landscapes arising as a result of two-way feedbacks between physical and biological processes.
We challenge the traditional interpretation of zonation as a one--way relation between dominant processes in the intertidal frame (i.e. competition vs. edaphic controls), which fails to capture the active role played by vegetation in engineering its own environment.
We use a point model of the coupled elevation-vegetation dynamics, which retains the description of the chief processes shaping these systems, to show how competing stable states are responsible for the formation of characteristic large-scale bio-geomorphic features in tidal landscapes worldwide.
Our analyses extended to a one-dimensional context allows us to explore the mechanism that leads to the formation of well-known, smaller-scale patterns associated with marsh vegetation species distributions.
We develop and present a model that for the first time incorporates species competition, species mutations, sediment transport and soil accretion in a spatially-extended setting, emphasizing that the formation of smaller-scale intertwined topographic and vegetation patterns are driven by bio-geomorphic feedbacks.
We finally analyze the robustness of large-scale and marsh-scale bio-geomorphic features to changes in the forcings, with implications for marsh ecosystem resilience to climate change and anthropogenic pressure
On the Strong Maximum Principle for Fully Nonlinear Degenerate Elliptic Equations
No full textWe prove a strong maximum principle for semicontinuous viscosity subsolutions or supersolutions of fully nonlinear degenerate elliptic PDE's, which complements the results of [17]. Our assumptions and conclusions are different from those in [17], in particular our maximum principle implies the nonexistence of a dead core. We test the assumptions on several examples involving the p-Laplacian and the minimal surface operator, and they turn out to be sharp in all cases where the existence of a dead core is known. We can also cover equations that are singular for p = 0 and very degenerate operators such as the 1-Laplacian and some first order Hamilton-Jacobi operators. 1. Introduction. In this note we investigate the validity of the Strong Maximum Principle and the Strong Minimum Principle (SMaxP and SMinP in the following) for semicontinuous viscosity subsolutions and supersolutions of fully nonlinear partial differential equations F (x; u; Du;D 2 u) = 0 (1) that are proper in the sen..
Symmetry properties of viscosity solutions to nonlinear uniformly elliptic equations
No full text\begin{abstract}We study uniformly elliptic fully nonlinear
equations
and prove results of Gidas-Ni-Nirenberg type for positive
viscosity solutions of such equations. We show that symmetries of
the equation and the domain are reflected by the solution, both in
bounded and unbounded domains
Vehicle and driver modeling and threat assessment for driving support functions
No full textThe article reports a novel method to assess the driving risk level and design a human friendly
warning strategy. The method is built on a Receding Horizon (RH) approach that is instanced for a
set of predefined driving scenarios such as driving in the lane, change lane, etc. In control field, the
RH is a technique that solves a sequence of optimization problemin real-time and, at each time step,
applies only the first value of the control plan to steer the system towards a desired behavior. In this
work, differentlythan in the control application, the initial value of the each control plan is used as a
measure of the correction that the rider should apply to conform to the computed optimal maneuver.
This choice has the advantage to provide an homogenous measure of the threat independently from
the scenario and it is directly linked with the control variable that the rider should use to accordingly
changethevehicledynamics. Additionally,theRH approachnaturallyaccommodatesroadgeometry
and attribute constraints, vehicle dynamics, driving input and styles. A proper development of the
vehicle model and a quantitative characterization of the human driving skills play an important role
in the method effectiveness. Additionally the method make use of a dedicated solver to compute the
probleminrealtime. Themethodwas appliedwithsuccess todevelopdrivingsupportfunctionsboth
for cars in the the FP6th European project PReVENT and the FP7th interactIVe and for motorcycles
in the FP7th European Project SAFERIDER.
The article introduces the RH approach as defined for the driving threat assessment. Then it
discusses in details the vehicle modelling requirements and how human driving skills are included
in the proposed method. Examplary use of how the system works in different driving scenario will
be given. Finally, the experimental results of pilot tests are shown for all the developed applications
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