A Lipschitz map f between the metric spaces X and Y is called a Lipschitz quotient map if there is a C > 0 (the smallest such C, the co-Lipschitz constant, is denoted coLip(f), while Lip(f) denotes the Lipschitz constant of f) so that for every x ∈ X and r > 0, fBX(x, r) ⊃ BY (f(x), r/C). Thus Lipschitz quotient maps are surjective maps which by definition have the property ensured by the open ...

For general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space B q ? , ? and satisfying a one-sided bound condition are unique within the class solutions. The exponent > 1 / 2 is universal independently nature nonlinearity regularity need only be imposed in when system expressed variables. proof utilises commutator estimate wh...

Consider a nonlocal conservation where the flux function depends on convolution of solution with given kernel. In singular local limit obtained by letting kernel converge to Dirac delta one formally recovers law. However, recent counter-examples show that in general solutions equations do not this work we focus laws modeling vehicular traffic: case, is anisotropic. We that, under fairly assumpt...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

There are many papers related to stability, some on suppression or on stabilization are one type of them. Functional differential systems are common and important in practice. They are special situations of neutral differential systems and generalization of ordinary differential systems. We discussed conditions on suppression on functional system with Markovian switching in our previous work: “...

We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for each initial condition. Our results extend those of previous works. For local existence and uniqueness, we only require the coefficients to be continuous and ...

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler–Maruyama (EM) method fails to...

Non-oscillatory schemes are widely used in numerical approximations of nonlinear conservation laws. The Nessyahu-Tadmor (NT) scheme is an example of a second order scheme that is both robust and simple. In this paper, we prove a new stability property of the NT scheme based on the standard minmod reconstruction in the case of a scalar strictly convex conservation law. This property is similar t...

This work is focused on the state of charge (SOC) estimation of a lithium-ion battery based on a nonlinear observer. First, the second-order resistor-capacitor (RC) model of the battery pack is introduced by utilizing the physical behavior of the battery. Then, for the nonlinear function of the RC model, a one-sided Lipschitz condition is proposed to ensure that the nonlinear function can play ...