Related papers: On expansions for nonlinear systems, error estimat…
This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality…
The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation expansion for general dissipative partial…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations…
We show that the grading of fields by conformal weight, when built into the initial group symmetry, provides a discrete, non-central conformal extension of any group containing dilatations. We find a faithful vector representation of the…
Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems.…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding C^2-maps on a compact Riemannian manifold M with uniform bounds on expansion factors and derivatives, we provide…
The time-convolutionless quantum master equation is an exact description of the nonequilibrium dynamics of open quantum systems, with the advantage of being local in time. We derive a perturbative expansion to arbitrary order in the…
This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…
This study presents a comprehensive spatial eigenanalysis of fully-discrete discontinuous spectral element methods, now generalizing previous spatial eigenanalysis that did not include time integration errors. The influence of discrete time…
In this paper, we consider the dual fractional parabolic problem in the right half space. We prove that the positive solutions are strictly increasing in $x_1$ direction without assuming the solutions be bounded. So far as we know, this is…
We obtain estimates on the continuous dependence on the coefficient for second order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and Gripenberg to…
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…