Related papers: Observability on lattice points for heat equations…
We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We…
This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems…
In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a…
Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic…
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
The aim of this article is to study the noncontrollability of the heat equation with double singular potential at an interior point and on the boundary of the domain.
We study a symmetry property of momentum distribution functions in the steady state of heat conduction. When the equation of motion is symmetric under change of signs for all dynamical variables, the distribution function is also symmetric.…
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit…
The collection of all topologies on the set of three points is studied treating the topology as quantum-like observable. It turns out to be possible under the assumption of the asymmetry between the spaces of bra- and ket-vectors. The…
We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain $$\Omega = (-1,1)\times\mathbb{T}\times\mathbb{T}$$ taking as observation regions slices of the form $\omega=(a,b) \times…
I give a brief introduction to the goals, challenges, and technical difficulties of lattice QCD thermodynamics and present some recent results from the HotQCD collaboration for the crossover temperature, equation of state, and other…
In the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system $w_t=w_{xx}$, $w(0,\cdot)=u$, $x>0$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a control.…
This paper presents a new observability estimate for parabolic equations in $\Omega\times(0,T)$, where $\Omega$ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\Omega$ and a subset…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
It is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is…
We derive in a direct and rather straightforward way the null controllability of a 2-D heat equation with boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the…
Equilibrium states of infinite extended lattice systems at high temperature are studied with respect to their entanglement. Two notions of separability are offered. They coincide for finite systems but differ for infinitely extended ones.…