291 research outputs found
Local null controllability of the N-dimensional Navier-Stokes system with N-1 scalar controls in an arbitrary control domain
In this paper we deal with the local null controllability of the
N-dimensional Navier-Stokes system with internal controls having one vanishing
component. The novelty of this work is that no condition is imposed on the
control domain
On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient
We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term grows slower than at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method
An optimization tool to design the field of a Solar Power Tower plant allowing heliostats of different sizes
The design of a Solar Power Tower plant involves the optimization of the heliostat field layout. Fields are usually designed to have all heliostats of identical size. Although the use of a single heliostat size has been questioned in the literature, there are no tools to design fields with heliostats of several sizes at the same time.
In this paper, the problem of optimizing the heliostat field layout of a system with heliostats of different sizes is addressed. We present an optimization tool to design solar plants allowing two heliostat sizes. The methodology is illustrated with a particular example considering different heliostat costs.MTM2013-41286-P (Spain)
MTM2015-65915-R (Spain)
P11-FQM-7603 (Andalucía)
TD1207 (EU COST Action
Some Inverse Problems for the Burgers Equation and Related Systems
In this article we deal with one-dimensional inverse problems concerning the
Burgers equation and some related nonlinear systems (involving heat effects
and/or variable density). In these problems, the goal is to find the size of
the spatial interval from some appropriate boundary observations of the
solution. Depending on the properties of the initial and boundary data, we
prove uniqueness and non-uniqueness results. In addition, we also solve some of
these inverse problems numerically and compute approximations of the interval
sizes
A parabolic approach to the control of opinion spreading
We analyze the problem of controlling to consensus a nonlinear system
modeling opinion spreading. We derive explicit exponential estimates on the
cost of approximately controlling these systems to consensus, as a function of
the number of agents N and the control time-horizon T. Our strategy makes use
of known results on the controllability of spatially discretized semilinear
parabolic equations. Both systems can be linked through time-rescalin
Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D
We prove global existence for a nonlinear Smoluchowski equation (a nonlinear
Fokker-Planck equation) coupled with Navier-Stokes equations in two dimensions.
The proof uses a deteriorating regularity estimate and the tensorial structure
of the main nonlinear terms
A parallel algorithm for solving the incompressible Navier-Stokes problems
AbstractWe introduce and analyze a parallel algorithm for solving the Navier-Stokes equations based on the splitting of the two main difficulties involved, the presence of nonlinear terms and the zero divergence condition. The numerical results obtained by using the proposed algorithm are quite consistent with those furnished by other known algorithms. Numerical results are discussed, as well as the advantages of this new algorithm
Local regularity for fractional heat equations
We prove the maximal local regularity of weak solutions to the parabolic
problem associated with the fractional Laplacian with homogeneous Dirichlet
boundary conditions on an arbitrary bounded open set
. Proofs combine classical abstract regularity
results for parabolic equations with some new local regularity results for the
associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756
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