scholarly journals Waves in Flexural Beams with Nonlinear Adhesive Interaction

2021 ◽  
Author(s):  
G. M. Coclite ◽  
G. Devillanova ◽  
F. Maddalena
Keyword(s):  
Dynamical Evolution ◽  
Elastic Beam ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Result ◽  
Time Behavior ◽  
Adhesive Interaction ◽  
Long Time ◽  
Initial Boundary Value ◽  
Main Effects

AbstractThe paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon of attachment-detachment of the beam occurring in adhesion phenomena. We prove existence of solutions in energy space and exhibit various counterexamples to uniqueness. Furthermore we characterize some relevant features of the solutions, ruling the main effects of the nonlinearity due to the elastic-breakable term on the dynamical evolution, by proving the linearization property according to Gérard (J Funct Anal 141(1):60–98, 1996) and an asymptotic result pertaining the long time behavior.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

scholarly journals Existence and long-time behavior of solutions to the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

2021 ◽  
Author(s):  
Nguyen Toan
Keyword(s):  
Stokes Equations ◽  
Dynamical Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Voigt Model ◽  
Initial Boundary Value

In this paper, we study the long-time dynamical behavior of the non-autonomous velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above-mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time-dependent forcing term $f \in L^2_b(\mathbb{R}; H^{-1}(\Omega))$ is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue, Wang (Comput. Math. Appl., 2020) in the case of non-autonomous and contain memory kernels which have not been studied before.

scholarly journals Global attractor for a class of nonlinear generalized Kirchhoff models

2016 ◽  
Vol 12 (8) ◽  
pp. 6452-6462 ◽  
Author(s):  
Penghui Lv ◽  
Jingxin Lu ◽  
Guoguang Lin
Keyword(s):  
Boundary Value Problem ◽  
Global Attractor ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Natural Energy ◽  
Long Time ◽  
Initial Boundary Value

The paper studies the long time behavior of solutions to the initial boundary value problem(IBVP) for a class of Kirchhoff models flow  .We establish the well-posedness, theexistence of the global attractor in natural energy space

scholarly journals Long-time behavior of solutions for a fractional diffusion problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ailing Qi ◽  
Die Hu ◽  
Mingqi Xiang
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Attractors ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
Initial Boundary Value

AbstractThis paper deals with the asymptotic behavior of solutions to the initial-boundary value problem of the following fractional p-Kirchhoff equation: $$ u_{t}+M\bigl([u]_{s,p}^{p}\bigr) (-\Delta )_{p}^{s}u+f(x,u)=g(x)\quad \text{in } \Omega \times (0, \infty ), $$ u t + M ( [ u ] s , p p ) ( − Δ ) p s u + f ( x , u ) = g ( x ) in  Ω × ( 0 , ∞ ) , where $\Omega \subset \mathbb{R}^{N}$ Ω ⊂ R N is a bounded domain with Lipschitz boundary, $N>ps$ N > p s , $0< s<1<p$ 0 < s < 1 < p , $M:[0,\infty )\rightarrow [0,\infty )$ M : [ 0 , ∞ ) → [ 0 , ∞ ) is a nondecreasing continuous function, $[u]_{s,p}$ [ u ] s , p is the Gagliardo seminorm of u, $f:\Omega \times \mathbb{R}\rightarrow \mathbb{R}$ f : Ω × R → R and $g\in L^{2}(\Omega )$ g ∈ L 2 ( Ω ) . With general assumptions on f and g, we prove the existence of global attractors in proper spaces. Then, we show that the fractal dimensional of global attractors is infinite provided some conditions are satisfied.

scholarly journals Strong Solutions of the Incompressible Navier–Stokes–Voigt Model

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 181
Author(s):  
Evgenii S. Baranovskii
Keyword(s):  
Three Dimensional ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Evolutionary Equation ◽  
Long Time ◽  
Special Basis ◽  
External Forces ◽  
Initial Boundary Value

This paper deals with an initial-boundary value problem for the Navier–Stokes–Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo–Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.

On the Transversal Vibrations of a Conveyor Belt Using a String-Like Equation

2001 ◽  
Author(s):  
Gede Suweken ◽  
W. T. van Horssen
Keyword(s):  
Wave Speed ◽  
Dynamical Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Conveyor Belt ◽  
Linear Wave ◽  
Long Time ◽  
Vertical Vibrations ◽  
Transversal Vibrations ◽  
Initial Boundary Value

Abstract In this paper an initial-boundary value problem for a linear wave (string) equation is considered. This problem can be used as a simple model to describe the vertical vibrations of a conveyor belt, for which the velocity is small with respect to the wave speed. In this paper the belt is assumed to move with varying speed. Formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt. It also will be shown that for this problem, the truncation method is not valid on long time scales.

Large time behavior in a forager–exploiter model with different taxis strategies for two groups in search of food

2019 ◽  
Vol 29 (11) ◽  
pp. 2151-2182 ◽  
Author(s):  
Youshan Tao ◽  
Michael Winkler
Keyword(s):  
Large Time ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Food Concentration ◽  
Large Time Behavior ◽  
Space Distribution ◽  
Time Behavior ◽  
Population Number ◽  
Initial Boundary Value ◽  
Two Populations

This work deals with a taxis cascade model for food consumption in two populations, namely foragers directly orienting their movement upward the gradients of food concentration and exploiters taking a parasitic strategy in search of food via tracking higher forager densities. As a consequence, the dynamics of both populations are adapted to the space distribution of food which is dynamically modified in time and space by the two populations. This model extends the classical one-species chemotaxis-consumption systems by additionally accounting for a second taxis mechanism coupled to the first in a consecutive manner. It is rigorously proved that for all suitably regular initial data, an associated Neumann-type initial-boundary value problem for the spatially one-dimensional version of this model possesses a globally defined bounded classical solution. Moreover, it is asserted that the considered two populations will approach spatially homogeneous distributions in the large time limit, provided that either the total population number of foragers or that of exploiters is appropriately small.

Sign in / Sign up

Export Citation Format

Share Document