相关论文: On the Stability Functional for Conservation Laws

Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…

The longitudinal structure function is considered at the next-to-leading order approximation using the expansion method, as defined by M.B.Gay Ducati and P.B.Goncalves [Phys.Lett.B {\bf390}, 401 (1997)] and further developed by Jingxuan…

We show that if $\phi$ is a continuous, minimally supported prescale function, then its translates are linearly independent on any set of positive measure in the unit interval. This generalizes results of Y. Meyer and P. G. Lemarie. This…

Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…

In kinetic theory, a system is usually described by its one-particle distribution function $f(\mathbf{r},\mathbf{v},t)$, such that $f(\mathbf{r},\mathbf{v},t)d\mathbf{r} d\mathbf{v}$ is the fraction of particles with positions and…

Stochastic non-local conservation law equation in the presence of discontinuous flux functions is considered in an $L^{1}\cap L^{2}$ setting. The flux function is assumed bounded and integrable (spatial variable). Our result is to prove…

Lyapunov stability theory is the bedrock of direct adaptive control. Fundamentally, Lyapunov stability requires constructing a distance-like function which must decrease with time to ensure stability. Feedback linearization, backstepping,…

The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…

Monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument. In this paper,…

In this paper we establish Functional Limit Theorems for the range of random walks in $\mathbb{Z}^d$ that are in the domain of attraction of a non-degenerate $\beta$-stable process in the weakly transient and recurrent regimes. These…

In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing…

We consider nonclassical entropy solutions to scalar conservation laws with concave-convex flux functions, whose set of left- and right-hand admissible states across undercompressive shocks is selected by a kinetic function \phi. We…

We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian…

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…

This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

For a dynamical system, it is known that the existence of a Lyapunov-type density function, called Lyapunov density or Rantzer's density function, implies convergence of Lebesgue almost all solutions to an equilibrium. Using the duality…

We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of…

A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…

We consider nondecreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to the Wasserstein distance of any order. This result extends…

Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…