Time periodic solutions to the beam equation with weak damping

2018 ◽  
Vol 59 (11) ◽  
pp. 111503
Author(s):  
Yu-Zhu Wang ◽  
Yanshuo Li
Keyword(s):  
Periodic Solutions ◽  
Beam Equation ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Weak Damping

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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