A5036065682- Stability and Controllability of Differential Equations
- Advanced Mathematical Physics Problems
- Navier-Stokes equation solutions
- Advanced Mathematical Modeling in Engineering
- Nonlinear Waves and Solitons
- Nonlinear Dynamics and Pattern Formation
- Quantum chaos and dynamical systems
- Nonlinear Differential Equations Analysis
- Optimization and Variational Analysis
- Differential Equations and Boundary Problems
- Model Reduction and Neural Networks
- Fluid Dynamics and Turbulent Flows
- Differential Equations and Numerical Methods
- Nonlinear Partial Differential Equations
- Mathematical Inequalities and Applications
- High-Voltage Power Transmission Systems
- Fixed Point Theorems Analysis
- Power Systems and Renewable Energy
- Mathematics and Applications
- Smart Grid and Power Systems
- Thermoelastic and Magnetoelastic Phenomena
- CO2 Sequestration and Geologic Interactions
- Global Health Care Issues
- Fuzzy and Soft Set Theory
- Fractional Differential Equations Solutions
Zhengzhou University
2015-2024
Harbin Institute of Technology
2024
Zhejiang Ocean University
2023
Zhejiang University
2023
Wuhan University
2015-2023
Sun Yat-sen University
2021-2022
Shandong University
2005-2011
Merck & Co., Inc., Rahway, NJ, USA (United States)
2008
Wyoming Department of Education
2007
University of Wyoming
2007
Abstract We consider a class of quasi‐linear evolution equations with non‐linear damping and source terms arising from the models viscoelasticity. By Galerkin approximation scheme combined potential well method we prove that when m < p , where (⩾0) are, respectively, growth orders strain term, under appropriate conditions, initial boundary value problem above‐mentioned admits global weak solutions decay to zero as t →∞. Copyright © 2002 John Wiley & Sons, Ltd.
In this paper, we are concerned with the existence and stability of pullback exponential attractors for a non-autonomous dynamical system. (ⅰ) We propose two new criteria discrete system continuous one, respectively. (ⅱ) By applying to Kirchhoff wave models structural damping supercritical nonlinearity construct family which stable respect perturbations.
The paper investigates the attractors and their robustness for a perturbed non-autonomous extensible beam equation with nonlinear nonlocal damping. We prove that related evolution process has finite-dimensional pullback attractor $ \mathscr{A}_\kappa exponential \mathscr{M}^\kappa_{exp} each extensibility parameter \kappa\in [0,1] $, respectively, both of them are stable on perturbation \kappa $. In particular, these stability holds global when dynamical system degenerates to an autonomous...
The paper studies the longtime behavior of solutions to initial boundary value problem (IBVP) for a class Kirchhoff models arising in elastoplastic flow utt−div{|∇u|m−1∇u}−Δut+Δ2u+h(ut)+g(u)=f(x). By combining decomposition idea with operate technique, it proves that under rather mild conditions, dynamical system associated above-mentioned IBVP possesses different phase spaces global attractor which is connected, respectively. For application, fact shows concerned permanent regime (global...
Abstract The paper studies the longtime behavior of solutions to initial boundary value problem (IBVP) for a nonlinear wave equation arising in elasto‐plastic flow u tt −div{|∇ | m −1 ∇ }−λΔ t +Δ 2 + g ( )= f x ). It proves that under rather mild conditions, dynamical system associated with above‐mentioned IBVP possesses global attractor, which is connected and has finite Hausdorff fractal dimension phase spaces X 1 = H (Ω) × L =( 3 (Ω)∩ (Ω)) (Ω), respectively. Copyright © 2008 John Wiley...
The paper studies the existence of global strong attractor for Kirchhoff type equations with nonlinear damping and supercritical nonlinearity utt−σ(‖∇u‖2)Δut−ϕ(‖∇u‖2)Δu+f(u)=h(x). It proves that in strictly positive stiffness factors case, there exists a finite-dimensional natural energy space endowed topology (rather than partially topology). result extends recent one achieved by Chueshov (2012).
The paper studies the existence of an exponential attractor for wave equation with structural damping and supercritical nonlinearity [Formula: see text]. By constructing a bounded absorbing set higher global regularity (rather than long-standing partial regularity) by using weak quasi-stability estimates strong ones as usual), we establish in natural energy space.
<p style='text-indent:20px;'>This paper investigates the existence of <i>strong</i> global and exponential attractors their robustness on perturbed parameter for an extensible beam equation with nonlocal energy damping in <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset{\mathbb R}^N $\end{document}</tex-math></inline-formula>: id="M2">\begin{document}$ u_{tt}+\Delta^2 u-\kappa\phi(\|\nabla u\|^2)\Delta u-M(\|\Delta...
This paper studies the existence and non-existence of global solutions to initial boundary value problems for non-linear wave equation utt + uxxxx = σ(ux)x f(x, t) Boussinesq-type σ(u)xx t). The proves that every above-mentioned problem has a unique solution under rather mild confining conditions, arrives at some sufficient conditions blow-up in finite time. Finally, few examples are given. Copyright © 2000 John Wiley & Sons, Ltd.
This paper studies the existence, regularity, and Hausdorff dimensions of global attractors for a class Kirchhoff models arising in elastoplastic flow utt−div{|∇u|m−1∇u}−Δut+Δ2u+h(ut)+g(u)=f(x). It proves that under rather mild conditions, dynamical system associated with above-mentioned possesses phase space X attractor which has further regularity Xσ1(↪↪X) finite dimension. For application, fact shows concerned permanent regime (global attractor) can be observed when excitation starts from...