scholarly journals A probabilistic view on the long-time behaviour of growth-fragmentation semigroups with bounded fragmentation rates

2021 ◽  
Author(s):  
Benedetta Cavalli
Keyword(s):  
Probabilistic Approach ◽  
Sufficient Conditions ◽  
Time Behaviour ◽  
Speed Of Convergence ◽  
Small Particles ◽  
Asymptotic Profile ◽  
Long Time Behaviour ◽  
Long Time ◽  
Fragmentation Equation ◽  
Necessary And Sufficient

The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. Bertoin and Watson ( $2018$ ) developed a probabilistic approach relying on the Feynman-Kac formula, that enabled them to answer to this question for sublinear growth rates. This assumption on the growth ensures that microscopic particles remain microscopic. In this work, we go further in the analysis, assuming bounded fragmentations and allowing arbitrarily small particles to reach macroscopic mass in finite time. We establish necessary and sufficient conditions on the coefficients of the equation that ensure Malthusian behaviour with exponential speed of convergence to the asymptotic profile. Furthermore, we provide an explicit expression of the latter.

scholarly journals Long-time behaviour of a thermomechanical model for adhesive contact

2011 ◽  
Vol 4 (2) ◽  
pp. 273-309 ◽  
Author(s):  
Elena Bonetti ◽  
◽  
Giovanna Bonfanti ◽  
Riccarda Rossi ◽  
◽  
...  
Keyword(s):  
Adhesive Contact ◽  
Time Behaviour ◽  
Thermomechanical Model ◽  
Long Time Behaviour ◽  
Long Time

Long time behaviour of diffusing particles in constrained geometries; application to chromatin motion

2006 ◽  
Vol 18 (14) ◽  
pp. S235-S243 ◽  
Author(s):  
A Rosa ◽  
F R Neumann ◽  
S M Gasser ◽  
A Stasiak
Keyword(s):  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

scholarly journals Long time behaviour of a singular phase transition model

2006 ◽  
Vol 15 (4) ◽  
pp. 1119-1135 ◽  
Author(s):  
Pavel Krejčí ◽  
◽  
Jürgen Sprekels
Keyword(s):  
Phase Transition ◽  
Transition Model ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

On the time periodic thermistor problem

2004 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
WALTER ALLEGRETTO ◽  
YANPING LIN ◽  
SHUQING MA
Keyword(s):  
Periodic Solutions ◽  
Degree Theory ◽  
Time Behaviour ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Galerkin Approximations ◽  
Long Time ◽  
Finite Dimensionality ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

Beobachtungen zum Stofftransport und zu einhergehenden Schädigungseffekten in porösen Baustoffen / Observations of mass transport and related deterioration mechanisms in porous building materials

2000 ◽  
Vol 6 (4) ◽  
pp. 451-462 ◽  
Author(s):  
L. Franke ◽  
R. Reimann-Oenel
Keyword(s):  
Building Materials ◽  
Life Time ◽  
Water Repellent ◽  
Historic Buildings ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time ◽  
Natural Stones ◽  
Coated Surfaces ◽  
Theoretical Considerations

Abstract It is reported about substance migration problems and their consequences, which have been investigated experimentally and which could be particularly relevant with regard to repair and restoration of historic buildings. One aim of the investigations was to find out, whether facades, treated with water repellent agents, showing non treated areas, can be affected in their long time behaviour. Such lacks can be due to non careful application of the repellent agent. In addition, investigations were made to find out. of coatings on salt containing mineral substrates, especially natural stones can reduce their life time. As a result of the experiments and the theoretical considerations, it follows, that a lack in water repellent treatment. could cause the risk of crust-development spallings in environment of non treated spots in the case that substrate is salt contaminated and moisture exchange takes place. All experiments with coatings, performed under the same conditions, show, that the coated surfaces have a more favourable behaviour than the same surfaces without coatings.

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