On the existence and uniqueness of time periodic solutions for a semilinear heat equation in the whole space

2016 ◽  
Vol 40 (3) ◽  
pp. 796-802
Author(s):  
Jian Deng
Keyword(s):  
Heat Equation ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Semilinear Heat Equation ◽  
Whole Space ◽  
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.

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