Analytic Fragmentation Semigroups and Classical Solutions to Coagulation–fragmentation Equations — a Survey

Banasiak, Jacek

doi:10.1007/s10114-018-7435-9

Cited by 4 publications

(2 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternatively, if the process is driven by the linear fragmentation part, it allows for more flexibility in selecting the fragmentation and transport parts, resulting in strong, classical solutions obtained within the framework of the semigroup theory. This has been shown in previous works [9][10][11]. This discrete system and its continuous counterpart have received considerable attention in the mathematics and physics literature in recent years; due to the enormous number of works devoted to them, we refer to the classical review [12] and the more recent [13] for an overview of the topic.…”

Section: Introductionmentioning

confidence: 75%

On the discrete Safronov–Dubovskiǐ coagulation equations: Well‐posedness, mass conservation, and asymptotic behavior

Ali,

Rai,

Giri

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

The global existence of mass‐conserving weak solutions to the Safronov–Dubovskiǐ coagulation equation is shown for the coagulation kernels satisfying at most linear growth for large sizes. In contrast to previous works, the proof mainly relies on the de la Vallée–Poussin theorem, which only requires the finiteness of the first moment of the initial condition. By showing the necessary regularity of solutions, it is shown that the weak solutions constructed herein are indeed classical solutions. Under additional restrictions on the initial data, the uniqueness of solutions is also shown. Finally, the continuous dependence on the initial data and the large‐time behavior of solutions are also addressed.

show abstract

Section: Introductionmentioning

confidence: 75%

On the discrete Safronov–Dubovskiǐ coagulation equations: Well‐posedness, mass conservation, and asymptotic behavior

Ali,

Rai,

Giri

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Alternatively, if the process is driven by the linear fragmentation part, it allows for more flexibility in selecting the fragmentation and transport parts, resulting in strong, classical solutions obtained within the framework of the semigroup theory. This has been shown in works such as [5,6,7]. This discrete system and its continuous counterpart have received considerable attention in the mathematics and physics literature in recent years; due to the enormous number of works devoted to them, we refer to the classical review [15] and the more recent [8] for an overview of the topic.…”

Section: Introductionmentioning

confidence: 99%

On the discrete Safronov-Dubovskii coagulation equation: well-posedness, mass-conservation and asymptotic behaviour

Ali

Rai

Giri

2023

Preprint

View full text Add to dashboard Cite

The global existence of mass-conserving weak solutions to the Safronov- Dubovskii coagulation equation is shown for the coagulation kernels satisfying at most linear growth for large sizes. In contrast to previous works, the proof mainly relies on the de la Vall ́ee-Poussin theorem [8, Theorem 7.1.6], which only requires the finiteness of the first moment of the initial condition. By showing the necessary regularity of solutions, it is shown that the weak solutions con- structed herein are indeed classical solutions. Under additional restrictions on the initial data, the uniqueness of solutions is also shown. Finally, the continu- ous dependence on the initial data and the large-time behaviour of solutions are also addressed. Mathematics Subject Classification(2020). Primary: 34A12, 34K30, 47J35; Secondary: 46B50.

show abstract

Exact asymptotic solution of an aggregation model with a bell-shaped distribution

Leyvraz

2021

Phys. Rev. E

View full text Add to dashboard Cite

Analytic Fragmentation Semigroups and Classical Solutions to Coagulation–fragmentation Equations — a Survey

Cited by 4 publications

References 62 publications

On the discrete Safronov–Dubovskiǐ coagulation equations: Well‐posedness, mass conservation, and asymptotic behavior

On the discrete Safronov–Dubovskiǐ coagulation equations: Well‐posedness, mass conservation, and asymptotic behavior

On the discrete Safronov-Dubovskii coagulation equation: well-posedness, mass-conservation and asymptotic behaviour

Exact asymptotic solution of an aggregation model with a bell-shaped distribution

Contact Info

Product

Resources

About