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509 Results Found

  • Feature Paper
  • Article
  • Open Access
275 Views
39 Pages

3 November 2025

In this paper, we study a hyperbolic–elliptic system with L1-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...

  • Feature Paper
  • Article
  • Open Access
2 Citations
1,789 Views
13 Pages

6 March 2023

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...

  • Feature Paper
  • Article
  • Open Access
2 Citations
1,848 Views
9 Pages

Hyers–Ulam Stability of a System of Hyperbolic Partial Differential Equations

  • Daniela Marian,
  • Sorina Anamaria Ciplea and
  • Nicolaie Lungu

23 June 2022

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.

  • Article
  • Open Access
1 Citations
1,422 Views
21 Pages

Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities

  • Rakhmatillo Djuraevich Aloev,
  • Abdumauvlen Suleimanovich Berdyshev,
  • Vasila Alimova and
  • Kymbat Slamovna Bekenayeva

17 May 2024

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...

  • Article
  • Open Access
1,260 Views
19 Pages

30 December 2023

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...

  • Article
  • Open Access
2 Citations
2,689 Views
17 Pages

8 September 2020

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...

  • Article
  • Open Access
2,407 Views
34 Pages

28 March 2021

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...

  • Article
  • Open Access
6 Citations
3,106 Views
9 Pages

3 March 2021

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...

  • Article
  • Open Access
32 Citations
4,298 Views
19 Pages

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...

  • Article
  • Open Access
4 Citations
1,227 Views
17 Pages

4 October 2023

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...

  • Article
  • Open Access
19 Citations
2,679 Views
13 Pages

19 January 2021

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...

  • Feature Paper
  • Article
  • Open Access
4 Citations
2,555 Views
17 Pages

20 April 2022

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...

  • Article
  • Open Access
1 Citations
2,131 Views
11 Pages

29 November 2021

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...

  • Review
  • Open Access
2 Citations
5,782 Views
18 Pages

4 February 2015

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...

  • Article
  • Open Access
16 Citations
5,389 Views
13 Pages

An Approach for the Generation of an Nth-Order Chaotic System with Hyperbolic Sine

  • Jizhao Liu,
  • Jun Ma,
  • Jing Lian,
  • Pengbin Chang and
  • Yide Ma

27 March 2018

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...

  • Article
  • Open Access
2 Citations
1,533 Views
11 Pages

Distributed Control for Non-Cooperative Systems Governed by Time-Fractional Hyperbolic Operators

  • Hassan M. Serag,
  • Areej A. Almoneef,
  • Mahmoud El-Badawy and
  • Abd-Allah Hyder

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...

  • Article
  • Open Access
11 Citations
10,016 Views
15 Pages

24 September 2008

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...

  • Article
  • Open Access
1 Citations
1,272 Views
16 Pages

10 October 2024

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...

  • Article
  • Open Access
7 Citations
3,106 Views
16 Pages

Circuit Implementation of a Modified Chaotic System with Hyperbolic Sine Nonlinearities Using Bi-Color LED

  • Christos K. Volos,
  • Lazaros Moysis,
  • George D. Roumelas,
  • Aggelos Giakoumis,
  • Hector E. Nistazakis and
  • George S. Tombras

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...

  • Article
  • Open Access
1,701 Views
18 Pages

10 June 2024

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...

  • Article
  • Open Access
2,903 Views
32 Pages

4 June 2024

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...

  • Article
  • Open Access
1,870 Views
13 Pages

Hyperbolicity of First Order Quasi-Linear Equations

  • Vladimir Vasilyev and
  • Yuri Virchenko

17 May 2022

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...

  • Article
  • Open Access
2 Citations
3,315 Views
21 Pages

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...

  • Article
  • Open Access
1 Citations
757 Views
21 Pages

14 August 2025

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...

  • Article
  • Open Access
3 Citations
3,014 Views
8 Pages

3 March 2021

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...

  • Article
  • Open Access
1 Citations
1,064 Views
28 Pages

12 October 2025

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...

  • Article
  • Open Access
2 Citations
2,491 Views
13 Pages

27 February 2020

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...

  • Article
  • Open Access
7 Citations
2,269 Views
14 Pages

An Extended Thermodynamics Model for Blood Flow

  • Elvira Barbera and
  • Annamaria Pollino

18 August 2022

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...

  • Article
  • Open Access
1 Citations
2,921 Views
25 Pages

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...

  • Article
  • Open Access
2 Citations
2,529 Views
15 Pages

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...

  • Article
  • Open Access
21 Citations
2,253 Views
22 Pages

31 July 2023

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...

  • Article
  • Open Access
3 Citations
2,105 Views
19 Pages

8 April 2022

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...

  • Article
  • Open Access
7 Citations
3,094 Views
25 Pages

9 February 2023

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-...

  • Article
  • Open Access
3 Citations
1,904 Views
22 Pages

31 May 2022

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...

  • Article
  • Open Access
4 Citations
5,725 Views
27 Pages

27 September 2017

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...

  • Article
  • Open Access
393 Views
17 Pages

3 November 2025

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...

  • Article
  • Open Access
1,323 Views
14 Pages

ω-Limit Sets of Impulsive Semigroups for Hyperbolic Equations

  • Petro Feketa,
  • Juliya Fedorenko,
  • Dmytro Bezushchak and
  • Anna Sukretna

27 September 2023

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...

  • Article
  • Open Access
3 Citations
2,738 Views
25 Pages

Four-Quadrant Riemann Problem for a 2×2 System II

  • Jinah Hwang,
  • Suyeon Shin,
  • Myoungin Shin and
  • Woonjae Hwang

10 March 2021

In previous work, we considered a four-quadrant Riemann problem for a 2×2 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...

  • Review
  • Open Access
5 Citations
2,375 Views
13 Pages

16 September 2021

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...

  • Article
  • Open Access
6 Citations
2,596 Views
15 Pages

Convergence and Numerical Solution of a Model for Tumor Growth

  • Juan J. Benito,
  • Ángel García,
  • María Lucía Gavete,
  • Mihaela Negreanu,
  • Francisco Ureña and
  • Antonio M. Vargas

11 June 2021

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...

  • Article
  • Open Access
19 Citations
4,450 Views
14 Pages

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...

  • Article
  • Open Access
6 Citations
2,780 Views
20 Pages

13 October 2023

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...

  • Article
  • Open Access
18 Citations
4,814 Views
16 Pages

7 July 2022

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...

  • Article
  • Open Access
1 Citations
1,222 Views
21 Pages

22 August 2024

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...

  • Article
  • Open Access
35 Citations
4,428 Views
21 Pages

18 November 2021

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...

  • Article
  • Open Access
6 Citations
2,441 Views
20 Pages

Computer Simulation of the Seismic Wave Propagation in Poroelastic Medium

  • Dana Bliyeva,
  • Dossan Baigereyev and
  • Kholmatzhon Imomnazarov

25 July 2022

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...

  • Article
  • Open Access
13 Citations
3,949 Views
17 Pages

20 August 2021

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...

  • Article
  • Open Access
4 Citations
2,101 Views
27 Pages

28 April 2025

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...

  • Article
  • Open Access
1 Citations
2,228 Views
14 Pages

6 May 2020

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

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