scholarly journals On the Instability of Stationary Solutions of a Lagrangian System with Gyroscopic Forces

1995 ◽  
Vol 115 (2) ◽  
pp. 350-367
Author(s):  
P. Negrini
Keyword(s):  
Stationary Solutions ◽  
Lagrangian System ◽  
Gyroscopic Forces

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

Periodic defect wall structures in irradiated solids: The spectrum of stationary solutions

1989 ◽  
Vol 40 (18) ◽  
pp. 12531-12534 ◽  
Author(s):  
H. Trinkaus ◽  
C. Abromeit ◽  
J. Villain
Keyword(s):  
Stationary Solutions ◽  
Wall Structures
Sign in / Sign up

Export Citation Format

Share Document