Controlling number of particles in fragmentation equations

Banasiak, Jacek; Noutchie, Suares Clovis Oukouomi

doi:10.1016/j.physd.2009.05.002

Cited by 8 publications

(13 citation statements)

References 19 publications

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“…Another stumbling block in the analysis of (1.1) was that there had been no results on semigroup generation in X 1 for fast growing fragmentation rates. This drawback was resolved in [26] for the case when b(x|y) = β(x)γ (y). This separability assumption played a key role in the analysis carried out in [26] as it meant that an explicit representation could be obtained for the resolvent of the fragmentation operator.…”

Section: Introductionmentioning

confidence: 99%

“…This drawback was resolved in [26] for the case when b(x|y) = β(x)γ (y). This separability assumption played a key role in the analysis carried out in [26] as it meant that an explicit representation could be obtained for the resolvent of the fragmentation operator. Clearly, this separability condition is satisfied for the class of so-called power-law fragmentation processes that we consider in this paper.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strong fragmentation and coagulation with power-law rates

Banasiak

Lamb²,

Langer³

2013

J Eng Math

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Existence of global classical solutions to fragmentation and coagulation equations with unbounded coagulation rates has been recently proved for initial conditions with finite higher order moments. These results cannot be directly generalized to the most natural space of solutions with finite mass and number of particles due to the lack of precise characterization of the domain of the generator of the fragmentation semigroup. In this paper we show that such a generalization is possible in the case when both fragmentation and coagulation are described by power-law rates which are commonly used in the engineering practice. This is achieved through direct estimates of the resolvent of the fragmentation operator, which in this case is explicitly known, proving that it is sectorial and carefully intertwining the corresponding intermediate spaces with appropriate weighted L1 spaces

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong fragmentation and coagulation with power-law rates

Banasiak

Lamb²,

Langer³

2013

J Eng Math

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“…Finally, we mention that in a recent paper [6], Banasiak and Oukoumi Noutchie have shown that the number of daughter particles produced by fragmentation remains finite for arbitrary fragmentation rates a and a class of separable size distribution functions b provided only thatů ∈ X 0,1 . This suggests that the results we present here may hold for more general initial conditions when b is a suitable separable function.…”

Section: Introductionmentioning

confidence: 93%

Global strict solutions to continuous coagulation–fragmentation equations with strong fragmentation

Banasiak

Lamb²

2011

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…with ] ∈ (−2, 0] (see also [5] for a more insight regarding this case). Note that the density of particles having mass at time is denoted by ( , ).…”

Section: Preliminariesmentioning

confidence: 99%

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

Noutchie

Goufo

2014

Mathematical Problems in Engineering

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We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.

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Controlling number of particles in fragmentation equations

Cited by 8 publications

References 19 publications

Strong fragmentation and coagulation with power-law rates

Strong fragmentation and coagulation with power-law rates

Global strict solutions to continuous coagulation–fragmentation equations with strong fragmentation

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

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