scholarly journals Long-Time Behaviour of Solutions for Autonomous Evolution Hemivariational Inequality with Multidimensional “Reaction-Displacement” Law

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Pavlo O. Kasyanov ◽  
Luisa Toscano ◽  
Nina V. Zadoianchuk
Keyword(s):  
Weak Solutions ◽  
Global Attractors ◽  
Hemivariational Inequalities ◽  
Time Behaviour ◽  
Evolution Inclusions ◽  
Long Time Behaviour ◽  
Long Time ◽  
Geophysical Processes ◽  
Positive Semiaxis ◽  
Autonomous Evolution

We consider autonomous evolution inclusions and hemivariational inequalities with nonsmooth dependence between determinative parameters of a problem. The dynamics of all weak solutions defined on the positive semiaxis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. New properties of complete trajectories are justified. We study classes of mathematical models for geophysical processes and fields containing the multidimensional “reaction-displacement” law as one of possible application. The pointwise behavior of such problem solutions on attractor is described.

Existence and long-time behaviour of weak solutions for the Mullins equation

2012 ◽  
Vol 75 (18) ◽  
pp. 6550-6561 ◽  
Author(s):  
Marina Chugunova ◽  
Roman Taranets
Keyword(s):  
Weak Solutions ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

Long-time behaviour of solutions to a one-dimensional strongly nonlinear model for phase transitions with micro-movements

2012 ◽  
Vol 142 (6) ◽  
pp. 1279-1307
Author(s):  
Jie Jiang
Keyword(s):  
Phase Transitions ◽  
Nonlinear Partial Differential Equation ◽  
Global Solutions ◽  
Global Attractors ◽  
Equation System ◽  
Time Behaviour ◽  
One Dimensional ◽  
Strongly Nonlinear ◽  
Long Time Behaviour ◽  
Long Time

This paper studies the long-time behaviour of solutions to a one-dimensional strongly nonlinear partial differential equation system arising from phase transitions with microscopic movements. Our system features a strongly nonlinear internal energy balance equation. Uniform bounds of the global solutions and the compactness of the orbit are obtained for the first time using a lemma established recently by Jiang. The existence of global attractors and convergence of global solutions to a single steady state as time goes to infinity are also proved.

scholarly journals Long-time behaviour of a thermomechanical model for adhesive contact

2011 ◽  
Vol 4 (2) ◽  
pp. 273-309 ◽  
Author(s):  
Elena Bonetti ◽  
◽  
Giovanna Bonfanti ◽  
Riccarda Rossi ◽  
◽  
...  
Keyword(s):  
Adhesive Contact ◽  
Time Behaviour ◽  
Thermomechanical Model ◽  
Long Time Behaviour ◽  
Long Time

Long time behaviour of diffusing particles in constrained geometries; application to chromatin motion

2006 ◽  
Vol 18 (14) ◽  
pp. S235-S243 ◽  
Author(s):  
A Rosa ◽  
F R Neumann ◽  
S M Gasser ◽  
A Stasiak
Keyword(s):  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

scholarly journals Long time behaviour of a singular phase transition model

2006 ◽  
Vol 15 (4) ◽  
pp. 1119-1135 ◽  
Author(s):  
Pavel Krejčí ◽  
◽  
Jürgen Sprekels
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

On the time periodic thermistor problem

2004 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
WALTER ALLEGRETTO ◽  
YANPING LIN ◽  
SHUQING MA
Keyword(s):  
Periodic Solutions ◽  
Degree Theory ◽  
Time Behaviour ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Galerkin Approximations ◽  
Long Time ◽  
Finite Dimensionality ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

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