Advances in Continuous and Discrete Models
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Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operatorsAbstract The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η -contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direction. Moreover, two examples are derived ... ...
Advances in Continuous and Discrete Models -
Random exponential attractor for a stochastic reaction-diffusion equation in $L^{2p}(D)$
Advances in Continuous and Discrete Models - Tập 2024 Số 1 - Trang 1-24 - 2024
In this paper, we establish some sufficient conditions for the existence of a random exponential attractor for a random dynamical system in a Banach space. As an application, we consider a stochastic reaction-diffusion equation with multiplicative noise. We show that the random dynamical system $\phi(t,\omega)$ generated by this stochastic reaction-diffusion equation is uniformly Fréchet different......
Convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-25 - 2022
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier–Stokes equations satisfying, in addition, the local energy inequality, and therefore suitable in the sense of Scheffer and Caffarelli–Kohn–Nirenberg. More precisely, we treat the space-periodic case in three space dimensions and consider a full discretization in which the classical Crank–Nicolson met......
Một bộ tích phân bậc hai với độ chính xác thấp cho phương trình Schrödinger phi tuyến Dịch bởi AI Tóm tắt Trong bài báo này, chúng tôi phân tích một bộ tích phân mới theo kiểu mũ cho phương trình Schrödinger phi tuyến bậc ba trên torus nhiều chiều d $\mathbb{T}^{d}$
T
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$H^{\gamma }(\mathbb{T}^{d})$
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$H^{\gamma +2}(\mathbb{T}^{d})$
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$\gamma > d/2$ hiện toàn bộ
Advances in Continuous and Discrete Models - Tập 2022 Số 1 - 2022
Stability of thermoelastic Timoshenko beam with suspenders and time-varying feedback
Advances in Continuous and Discrete Models - Tập 2023 - Trang 1-19 - 2023
This paper considers a one-dimensional thermoelastic Timoshenko beam system with suspenders, general weak internal damping with time varying coefficient, and time-varying delay terms. Under suitable conditions on the nonlinear terms, we prove a general stability result for the beam model, where exponential and polynomial decay are special cases. We also gave some examples to illustrate our theoret......
Computing confined elasticae
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-16 - 2022
We devise a numerical scheme for computing arc-length parameterized curves of low bending energy that are confined to convex domains. We address the convergence of the discrete formulations to a continuous model and the unconditional stability of an iterative scheme. Numerical simulations confirm the theoretical results and lead to a classification of observed optimal curves within spheres.
Switched hyperbolic balance laws and differential algebraic equations
Advances in Continuous and Discrete Models - Tập 2023 - Trang 1-31 - 2023
Motivated by several applications, we investigate the well-posedness of a switched system composed by a system of linear hyperbolic balance laws and by a system of linear algebraic differential equations. This setting includes networks and looped systems of hyperbolic balance laws. The obtained results are globally in time, provided that the inputs have finite (but not necessarily small) total var......
Path classification by stochastic linear recurrent neural networksAbstract We investigate the functioning of a classifying biological neural network from the perspective of statistical learning theory, modelled, in a simplified setting, as a continuous-time stochastic recurrent neural network (RNN) with the identity activation function. In the purely stochastic (robust) regime, we give a generalisation error bound that holds with ... ...
Advances in Continuous and Discrete Models - - 2022
On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-18 - 2022
In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of o......
H∞ observer-based sliding mode control for uncertain discrete-time singularly perturbed systems
Advances in Continuous and Discrete Models - Tập 2023 - Trang 1-17 - 2023
This paper studies the sliding mode control (SMC) problem of discrete-time singularly perturbed systems (DTSPSs) with external perturbations and nonlinear inputs. First, to estimate the state of the original system, a novel state observer is constructed. Under this condition, the observer error system is ensured to be input-to-state stable (ISS) and satisfies the given H∞ performance index. Then, ......
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