Results 11 to 20 of about 404 (49)

Global attractors for nonlinear viscoelastic equations with memory [PDF]

, 2013
We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos.
Conti, Monica, Marchini, Elsa M., Pata, Vittorino   +2 more
core   +1 more source

On the strongly damped wave equation and the heat equation with mixed boundary conditions

Abstract and Applied Analysis, Volume 5, Issue 3, Page 175-189, 2000., 2000
We study two one‐dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
Aloisio F. Neves
wiley   +1 more source

The asymptotic behaviors of solutions for higher-order (m1, m2)-coupled Kirchhoff models with nonlinear strong damping

Demonstratio Mathematica, 2023
The Kirchhoff model is derived from the vibration problem of stretchable strings. This article focuses on the long-time dynamics of a class of higher-order coupled Kirchhoff systems with nonlinear strong damping.
Lv Penghui, Lin Guoguang, Lv Xiaojun
doaj   +1 more source

Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts [PDF]

, 2018
We study the asymptotic behaviour of the following linear growth-fragmentation equation$$\dfrac{\partial}{\partial t} u(t,x) + \dfrac{\partial}{\partial x} \big(x u(t,x)\big) + B(x) u(t,x) =4 B(2x)u(t,2x),$$ and prove that under fairly general ...
Bernard, Etienne, Doumic, Marie, Gabriel, Pierre   +2 more
core   +4 more sources

Random uniform exponential attractor for stochastic non-autonomous reaction-diffusion equation with multiplicative noise in ℝ3

Open Mathematics, 2019
We first introduce the concept of the random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system (NRDS) and give a theorem on the existence of the random uniform exponential attractor for a jointly continuous ...
Han Zongfei, Zhou Shengfan
doaj   +1 more source

Sharp estimates for the global attractor of scalar reaction-diffusion equations with a Wentzell boundary condition [PDF]

, 2011
In this paper, we derive optimal upper and lower bounds on the dimension of the attractor AW for scalar reaction-diffusion equations with a Wentzell (dynamic) boundary condition.
Gal, Ciprian G.
core   +1 more source

Time-dependent attractors for non-autonomous nonlocal reaction-diffusion equations [PDF]

, 2018
In this paper, the existence and uniqueness of weak and strong solutions for a non-autonomous nonlocal reaction-diffusion equation is proved. Next, the existence of minimal pullback attractors in the L2 -norm in the frameworks of universes of fixed ...
Caraballo Garrido, Tomás, Herrera Cobos, Marta, Marín Rubio, Pedro   +2 more
core   +1 more source

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations [PDF]

, 2011
The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$.
Abraham R., Angenent S. B., Angenent S. B., Angenent S. B., Anosov D. V., Arroyo A., Bendixson I., Bonatti C., Bonatti C., Bonatti C., Brunovský P., Brunovský P., Brunovský P., Brunovský P., Chen X.-Y., Crovisier S., Czaja R., Dancer E. N., Fiedler B., Fiedler B., Fiedler B., Fiedler B., Fiedler B., Fusco G., Fusco G., Fusco G., Fusco G., Galaktianov V. A., GENEVIÈVE RAUGEL, Ghrist R. W., Guckenheimer J., Hale J. K., Hale J. K., Hardt R., Hayashi S., Henry D., Henry D. B., Hirsch M. W., Hirsch M. W., Hirsch M. W., Hirsch M. W., Jolly M., Joly R., Joly R., Joly R., Mallet-Paret J., Matano H., Matano H., Matano H., Newhouse S. E., Nickel K., Nitecki Z., Palis J., Peixoto M. M., Peixoto M. M., Poláčik P., Poláčik P., Poláčik P., Poláčik P., Prizzi M., Pugh C. C., Pugh C. C., Pugh C. C., Pujals E. R., Robinson C., Robinson J. C., Rocha C., Rocha C., ROMAIN JOLY, Ruelle D., Sandstede B., Smale S., Smale S., Smale S., Smale S., Smillie J., Smith H. L., Smith H. L., Sturm C., Wolfrum M.   +79 more
core   +4 more sources

Global attractors for the one dimensional wave equation with displacement dependent damping

, 2010
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a global ...
Arrietta, Babin, Belleri, Gatti, Ghidaglia, Ladyzhenskaya, Lions, Pata, Pata, Pata, Temam   +10 more
core   +1 more source

Existence and stability of fourth-order nonlinear plate problem

Nonautonomous Dynamical Systems, 2019
In this paper, we study a fourth-order plate problem as a model for a suspension bridge in the presence of a nonlinear frictional damping and a hanger restoring force. We establish the existence of a global weak solution and prove a stability result.
Messaoudi Salim A., Mukiawa Soh Edwin
doaj   +1 more source