scholarly journals Time-Periodic Solutions of the Burgers Equation

2007 ◽  
Vol 11 (2) ◽  
pp. 303-323 ◽  
Author(s):  
Magnus Fontes ◽  
Olivier Verdier
Keyword(s):  
Periodic Solutions ◽  
Burgers Equation ◽  
Time Periodic Solutions ◽  
Time Periodic

scholarly journals ON TIME PERIODIC SOLUTIONS TO THE GENERALIZED BBM-BURGERS EQUATION WITH TIME-DEPENDENT PERIODIC EXTERNAL FORCE

2020 ◽  
Vol 25 (2) ◽  
pp. 184-197
Author(s):  
Yinxia Wang
Keyword(s):  
Periodic Solutions ◽  
External Force ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Space Dimension ◽  
Burgers Equation ◽  
Time Dependent ◽  
Contraction Mapping Theorem ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper, we consider the generalized BBM-Burgers equation with periodic external force in Rn. Existence and uniqueness of time periodic solutions that have the same period as the external force are established in some suitable function space for the space dimension n≥ 3. Moreover, we also discuss the time asymptotic stability of the time periodic solution. The proof is mainly based on the contraction mapping theorem and continuous argument.

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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