Long Time Behavior of Periodic Solutions to Scalar Conservation Laws in Several Space Dimensions

2013 ◽  
Vol 45 (4) ◽  
pp. 2064-2070 ◽  
Author(s):  
Constantine M. Dafermos
Keyword(s):  
Conservation Laws ◽  
Periodic Solutions ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Scalar Conservation Laws ◽  
Long Time ◽  
Scalar Conservation

scholarly journals Anti-periodic problem for semilinear differential inclusions involving Hille-Yosida operators

2021 ◽  
pp. 1-31
Author(s):  
Nguyen Thi Van Anh ◽  
Tran Dinh Ke ◽  
Do Lan
Keyword(s):  
Periodic Solutions ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Periodic Problem ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Multivalued Maps ◽  
Integrated Semigroups ◽  
Long Time ◽  
Theoretical Results

In this paper we are interested in the anti-periodic problem governed by a class of semilinear differential inclusions with linear parts generating integrated semigroups. By adopting the Lyapunov-Perron method and the fixed point argument for multivalued maps, we prove the existence of anti-periodic solutions. Furthermore, we study the long-time behavior of mild solutions in connection with anti-periodic solutions. Consequently, as the nonlinearity is of single-valued, we obtain the exponential stability of anti-periodic solutions. An application of theoretical results to a class of partial differential equations will be given.

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