Finite Speed of Propagation and Waiting Time for Local Solutions of Degenerate Equations in Viscoelastic Media or Heat Flows with Memory

2016 ◽  
Vol 2 (1-2) ◽  
pp. 207-216
Author(s):  
S. N. Antontsev ◽  
J. I. Díaz
Keyword(s):  
Waiting Time ◽  
Finite Speed Of Propagation ◽  
Heat Flows ◽  
Viscoelastic Media ◽  
Finite Speed ◽  
Degenerate Equations ◽  
Local Solutions ◽  
Speed Of Propagation ◽  
With Memory

scholarly journals Finite speed of propagation and waiting time for a thin-film Muskat problem

2017 ◽  
Vol 147 (4) ◽  
pp. 813-830 ◽  
Author(s):  
Philippe Laurençot ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Thin Film ◽  
Initial Data ◽  
Waiting Time ◽  
Scale Invariance ◽  
Sufficient Conditions ◽  
Two Phase ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Muskat Problem ◽  
Speed Of Propagation

Propagation at a finite speed is established for non-negative weak solutions to a thin-film approximation of the two-phase Muskat problem. The expansion rate of the support matches the scale invariance of the system. Moreover, we determine sufficient conditions on the initial data for the occurrence of waiting time phenomena.

scholarly journals Comparison and maximum principles for a class of flux-limited diffusions with external force fields

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Manh Hong Duong
Keyword(s):  
Maximum Principle ◽  
External Force ◽  
Force Fields ◽  
Gradient Flow ◽  
Strong Maximum Principle ◽  
Maximum Principles ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Transportation Theory ◽  
Speed Of Propagation

AbstractIn this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal transportation theory. We first provide an argument to incorporate the external force fields. Then, we are concerned with comparison and maximum principles for this equation. We consider both stationary and evolutionary problems. We show that the former satisfies a comparison principle and a strong maximum principle while the latter fulfils weaker ones. The key technique is a transformation that matches well with the gradient flow structure of the equation.

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