Instability of Stationary Solutions of Evolution Equations on Graphs Under Dynamical Node Transition

Author(s):  
Joachim von Below ◽  
Baptiste Vasseur
2006 ◽  
Vol 6 (6) ◽  
pp. 1199-1212 ◽  
Author(s):  
Tomás Caraballo ◽  
◽  
P.E. Kloeden ◽  
B. Schmalfuss ◽  
◽  
...  

2007 ◽  
Vol 18 (2/3, June) ◽  
pp. 271-293 ◽  
Author(s):  
B. Schmalfuss ◽  
M. Garrido-Atienza ◽  
Tomás Caraballo

2000 ◽  
Vol 11 (07) ◽  
pp. 1283-1295 ◽  
Author(s):  
G. MEDEIROS ◽  
M. A. IDIART ◽  
R. M. C. DE ALMEIDA

We consider the Penna model for biological aging to investigate correlations between early fertility and late life survival rates in populations at equilibrium. We consider inherited initial reproduction ages together with a reproduction cost translated in a probability that mother and offspring die at birth, depending on the mother age. For convenient sets of parameters, the equilibrated populations present genetic variability in what regards both genetically programmed death age and initial reproduction age. In the asexual Penna model, a negative correlation between early life fertility and late life survival rates naturally emerges in the stationary solutions. In the sexual Penna model, selection experiments are performed where individuals are sorted by initial reproduction age from the equilibrated populations and the separated populations are evolved independently. After a transient, a negative correlation between early fertility and late age survival rates also emerges in the sense that populations that start reproducing earlier present smaller average genetically programmed death age. These effects appear due to the age structure of populations in the steady state solution of the evolution equations. We claim that the same demographic effects may be playing an important role in selection experiments in the laboratory.


2017 ◽  
Vol 9 (3) ◽  
pp. 1
Author(s):  
Jeng-Eng Lin

We show that there are no nontrivial stationary solutions of certain decay order for some applied nonlinear evolution equations which include the thin epitaxial film model with slope selection and the square phase field crystal (SPFC) equation. The method is to use the Morawetz multiplier and the Gagliardo-Nirenberg inequality.


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