scholarly journals Multiple Front Propagation in a Potential Non-Gradient System

1996 ◽  
pp. 85-97
Author(s):  
M. San Miguel ◽  
R. Montagne ◽  
A. Amengual ◽  
E. Hernández-García
Keyword(s):  
Front Propagation ◽  
Gradient System

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

scholarly journals Genetic recombination as a generalised gradient flow

2021 ◽  
Author(s):  
Frederic Alberti
Keyword(s):  
Arbitrary Number ◽  
Genetic Recombination ◽  
Reaction Network ◽  
Gradient Flow ◽  
Mass Action ◽  
Gradient System ◽  
Gradient Structure ◽  
Law Of Mass Action ◽  
Reversible Chemical Reaction ◽  
Time Partitioning

AbstractIt is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.

scholarly journals The temperature dependence of gradient system response characteristics

2019 ◽  
Vol 83 (4) ◽  
pp. 1519-1527 ◽  
Author(s):  
Manuel Stich ◽  
Christiane Pfaff ◽  
Tobias Wech ◽  
Anne Slawig ◽  
Gudrun Ruyters ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
System Response ◽  
Gradient System ◽  
Response Characteristics

Infiltration-mediated combustion in quasi-2D geometry: Stability of front propagation

2010 ◽  
Vol 19 (2) ◽  
pp. 79-84 ◽  
Author(s):  
P. M. Krishenik ◽  
N. I. Ozerkovskaya ◽  
A. N. Firsov ◽  
K. G. Shkadinsky
Keyword(s):  
Front Propagation
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