509 Results Found

In this paper, we study a hyperbolic–elliptic system with $L^1$-initial data, which arises as a mathematical model for chemotaxis. In particular, after introducing the notion of entropy solutions in this setting, we prove results concerning the ex...

We address a hyperbolic model for prey-sensitive predators interacting with purely diffusive prey. We adopt the Cattaneo formulation for describing the predators’ transport. Given the hyperbolicity, the long-lived short-wave patterns occur for...

In this paper, we study Hyers–Ulam and generalized Hyers–Ulam–Rassias stability of a system of hyperbolic partial differential equations using Gronwall’s lemma and Perov’s theorem.

In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary c...

We consider two abstract systems of parabolic–hyperbolic type that model thermoelastic problems. We study the influence of the physical constants and the initial data on the nonexistence of global solutions that, in our framework, are produced...

In this paper, we consider a class of first-order hyperbolic distributed parameter systems. Our focus is on the design of a new class of model predictive control schemes using a quasi-Shannon wavelet basis. First, the first-order hyperbolic distribut...

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizu...

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations...

In this paper, new algorithms called the “Modified exp(−Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp(−Ω(ξ))-expansion method; the latter is based on th...

In this paper, we introduce a numerical integration method for hyperbolic systems problems known as the splitting method, which serves as an effective tool for solving complex multidimensional problems in mathematical physics. The exponential stabili...

We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite...

We address a hyperbolic predator–prey model, which we formulate with the use of the Cattaneo model for chemosensitive movement. We put a special focus on the case when the Cattaneo equation for the flux of species takes the form of conservation law—t...

This paper discusses the iterative learning control problem for a class of non-linear partial difference system hyperbolic types. The proposed algorithm is the PD-type iterative learning control algorithm with initial state learning. Initially, we in...

Currently, there is great renewed interest in proving the topological transitivity of various classes of continuous dynamical systems. Even though this is one of the most basic dynamical properties that can be investigated, the tools used by various...

Chaotic systems with hyperbolic sine nonlinearity have attracted the attention of researchers in the last two years. This paper introduces a new approach for generating a class of simple chaotic systems with hyperbolic sine. With nth-order ordinary d...

This paper studies distributed optimal control for non-cooperative systems involving time-fractional hyperbolic operators. Through the application of the Lax–Milgram theorem, we confirm the existence and uniqueness of weak solutions. Central to...

We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the e...

The positioning algorithms of the Enhanced Long-Range Navigation (eLoran) system primarily include the hyperbolic positioning algorithm and the pseudorange positioning algorithm. However, the calculations present in the existing literature are inaccu...

In this paper, a chaotic three dimansional dynamical system is proposed, that is a modification of the system in Volos et al. (2017). The new system has two hyperbolic sine nonlinear terms, as opposed to the original system that only included one, in...

Complex aviation systems’ integrity deteriorates over time due to operational factors; hence, the ability to forecast component remaining useful life (RUL) is vital to their optimal operation. Data-driven prognostic models are essential for sys...

Step-stare imaging systems are widely used in aerospace optical remote sensing. In order to achieve fast scanning of the target region, efficient coverage path planning (CPP) is a key challenge. However, traditional CPP methods are mostly designed fo...

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient condit...

In this article, we consider a delayed system of first-order hyperbolic differential equations. The presence of the delay term in first-order hyperbolic delay differential equations poses significant challenges in both analysis and numerical solution...

Stochastic resonance (SR) systems possess the remarkable ability to enhance weak signals by transferring noise energy into the signal, and thus have significant application prospects in weak signal detection. However, the classic bistable SR (CBSR) s...

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsi...

This study introduces an innovative self-regulating intelligent optimal balancing control framework for inverted pendulum-type mechatronic platforms, designed to enhance reference tracking accuracy and improve disturbance rejection capability. The co...

It is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically oriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural notion of symmetry for cocycles. It is discussed the...

A model for blood flow is introduced in the context of the Rational Extended Thermodynamics (RET). The balance equations are applied to the two-hierarchy structure recently introduced by Ruggeri and Sugiyama. The constitutive relations are derived wi...

We show that a two-dimensional area-preserving map with Lorentzian potential is a topological horseshoe and uniformly hyperbolic in a certain parameter region. In particular, we closely examine the so-called sector condition, which is known to be a s...

In this paper, we consider a system of one-dimensional hyperbolic delay differential equations (HDDEs) and their corresponding initial conditions. HDDEs are a class of differential equations that involve a delay term, which represents the effect of p...

It is well known that, compared to low-dimension chaotic systems, three-dimensional chaotic systems have a wider parameter range, more complicated behaviour, and better unpredictability. This fact motivated us to introduce a novel image encryption me...

This paper deals with the Cauchy problem for a class of first-order semilinear hyperbolic equations of the form ${\partial }_t{f}_i+{\sum }_{j=1}^d{\lambda }_{ij}{\partial }_{x_j}{f}_i=Q_i\left(f\right).$ where $f_i=f_i(x,t)$ ($i=1,\cdots ,n$) and $x=(x_1,\cdots ,x_d)\in {\mathrm{I}\mathrm{R}}^d$ ($n\ge 2,d\ge 1$). Under assu...

In this paper, a novel flow tracking control scheme for particleboard glue system with complex disturbance and unmeasurable system state is investigated. The method is based on hyperbolic tangent extended state observer and adaptive fuzzy fractional...

In this paper, we present a new explicit second-order accurate structure-preserving finite volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg equations. The model combines the unified Godunov-Peshkov-...

This paper focuses on the tracking control problem for a family of fractional-order systems with unknown drift functions and unknown time delays. By employing fuzzy logic systems (FLSs), the unknown functions are approximated and compensated. Meanwhi...

A new method to describe hyperbolic patterns in two-dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties of being covariant with the dynamics, and thus, being mapped by the tangent lin...

In this paper, we prove that the Taylor expansions of analytic functions appearing in the linearization of quadratic maps at hyperbolic fixed points do not successfully approximate invariant manifolds, such as stable and unstable manifolds, when high...

In this paper, we investigate the qualitative behavior of an evolutionary problem consisting of a hyperbolic dissipative equation whose trajectories undergo instantaneous impulsive discontinuities at the moments when the energy functional reaches a c...

In previous work, we considered a four-quadrant Riemann problem for a $2\times 2$ hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave. In t...

This paper is concerned with modeling nonequilibrium phenomena in spatial domains with boundaries. The resultant models consist of hyperbolic systems of first-order partial differential equations with boundary conditions (BCs). Taking a linearized mo...

In this paper, we show the application of the meshless numerical method called “Generalized Finite Diference Method” (GFDM) for solving a model for tumor growth with nutrient density, extracellular matrix and matrix degrading enzymes, [recently propo...

We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximati...

A new macroscopic traffic system is devised that observes the transition distance between the vehicles and driver sensitivity during traffic evolution. The driver sensitivity in this system is based on the traversed time over a 200 m road section and...

For the problem of the system state variable taking a long time to reach the sliding mode surface and the chattering frequency being high in the sliding mode surface, a sliding mode control method based on the adaptive reaching law is proposed, the s...

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in spa...

In order to reduce vehicle vibration during driving conditions, a fuzzy sliding mode control strategy (FSMC) for semi-active air suspension based on the magnetorheological (MR) damper is proposed. The MR damper used in the semi-active air suspension...

This article presents an algorithm for the numerical solution of an initial-boundary value problem for a symmetric t-hyperbolic system of partial differential equations. This problem is based on continual filtration model, which describes the propaga...

This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving c...

The underwater conditions of the coastal ecosystem require careful monitoring to anticipate potential environmental hazards. Moreover, the unique characteristics of the marine underwater environment have presented numerous challenges for the advancem...

In this paper, we develop an accurate technique via the use of the Adomian decomposition method (ADM) to solve analytically a $2\times 2$ systems of partial differential equation that represent balance laws of hyperbolic-elliptic type. We pro...