2,296 research outputs found
Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations
In this paper we make a subtle use of operator theory techniques and the
well-known Schauder fixed-point principle to establish the existence of
pseudo-almost automorphic solutions to some second-order damped
integro-differential equations with pseudo-almost automorphic coefficients. In
order to illustrate our main results, we will study the existence of
pseudo-almost automorphic solutions to a structurally damped plate-like
boundary value problem.Comment: 20 pages. arXiv admin note: substantial text overlap with
arXiv:1402.563
Global regularity and probabilistic schemes for free boundary surfaces of multivariate American derivatives and their Greeks
In a rather general setting of multivariate stochastic volatility market
models we derive global iterative probabilistic schemes for computing the free
boundary and its Greeks for a generic class of American derivative models using
front-fixing methods. Convergence is closely linked to a proof of global
regularity of the free boundary surface
Backstepping PDE Design: A Convex Optimization Approach
Abstract\u2014Backstepping design for boundary linear PDE is
formulated as a convex optimization problem. Some classes of
parabolic PDEs and a first-order hyperbolic PDE are studied,
with particular attention to non-strict feedback structures. Based
on the compactness of the Volterra and Fredholm-type operators
involved, their Kernels are approximated via polynomial
functions. The resulting Kernel-PDEs are optimized using Sumof-
Squares (SOS) decomposition and solved via semidefinite
programming, with sufficient precision to guarantee the stability
of the system in the L2-norm. This formulation allows optimizing
extra degrees of freedom where the Kernel-PDEs are included
as constraints. Uniqueness and invertibility of the Fredholm-type
transformation are proved for polynomial Kernels in the space
of continuous functions. The effectiveness and limitations of the
approach proposed are illustrated by numerical solutions of some
Kernel-PDEs
A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances
This note addresses input-to-state stability (ISS) properties with respect to
(w.r.t.) boundary and in-domain disturbances for Burgers' equation. The
developed approach is a combination of the method of De~Giorgi iteration and
the technique of Lyapunov functionals by adequately splitting the original
problem into two subsystems. The ISS properties in -norm for Burgers'
equation have been established using this method. Moreover, as an application
of De~Giorgi iteration, ISS in -norm w.r.t. in-domain disturbances
and actuation errors in boundary feedback control for a 1- {linear}
{unstable reaction-diffusion equation} have also been established. It is the
first time that the method of De~Giorgi iteration is introduced in the ISS
theory for infinite dimensional systems, and the developed method can be
generalized for tackling some problems on multidimensional spatial domains and
to a wider class of nonlinear {partial differential equations (PDEs)Comment: This paper has been accepted for publication by IEEE Trans. on
Automatic Control, and is available at
http://dx.doi.org/10.1109/TAC.2018.2880160. arXiv admin note: substantial
text overlap with arXiv:1710.0991
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