Structural stability of disperse systems and finite nature of a coagulation front

Dubovski, Pavel B.

doi:10.1134/1.558995

Cited by 14 publications

(12 citation statements)

References 12 publications

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“…Lemma 2.6. Consider T ∈ (0, ∞), i ∈ N and c n i (t) satisfies (6). The following result holds true for a constant Q(T ) which depends on ||c 0 ||, α and T :…”

Section: Non-conservative Truncation and Required Resultsmentioning

confidence: 99%

“….) and let it be identified with the point of R n obtained by discarding the j th components, for j > n. Let c n be the solution of the n-dimensional truncated system ( 13)-( 16) with initial condition c n (0) = c n 0 , both satisfying (6). Assume φ i,j ≤ ij, ∀i, j ≥ 1 and let Ω n m (t) be defined by…”

Section: Conservative Truncation and Required Resultsmentioning

confidence: 99%

“…The Safronov-Dubovski coagulation equation, which is actually the discrete version of the OHS equation, was introduced by P.B. Dubovski [4] in 1999 and then further studied by authors namely Bagland [5], Dubovski [6,7] and Davidson [8,9]. The equation is expressed as…”

Section: Prologuementioning

confidence: 99%

“…Dubovski [6], in 1999, developed the model (2) and demonstrated preliminary results for the general kernel φ i,j including the non-negativity and mass conservation law. The author also discussed the significance of the Oort-Hulst-Safronov model in calculating coagulation front velocity (the rate of displacement of the boundary of the non-zero values of the distribution function).…”

Section: Existing Literaturementioning

confidence: 99%

“…They discovered that the self-similar profiles were compactly supported and had the discontinuity at the edge of their support. Laurençot [20] analysed the OHS model and discussed collapse (gelation from astrophysical point of view [6]) and established the self similar profiles for the product kernel φ(x, y) = xy. In 2020, Barik et al [21] proved the existence of weak mass conserving solutions to the OHS equation ( 1) for the singular kernel.…”

Section: Existing Literaturementioning

confidence: 99%

See 4 more Smart Citations

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Kaushik¹,

Kumar²

2022

Preprint

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The article presents the existence and mass conservation of solution for the discrete Safronov-Dubovski coagulation equation for the product coalescence coefficients φ such that φ i,j ≤ ij ∀ i, j ∈ N. Both conservative and non-conservative truncated systems are used to analyse the infinite system of ODEs. In the conservative case, Helly's selection theorem is used to prove the global existence while for the non-conservative part, we make use of the refined version of De la Vallée-Poussin theorem to establish the existence. Further, it is shown that these solutions conserve density. Finally, the solutions are shown to be unique when the kernel φ i,j ≤ min{i η , j η } where η ∈ [0, 2].

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“…Lemma 2.6. Consider T ∈ (0, ∞), i ∈ N and c n i (t) satisfies (6). The following result holds true for a constant Q(T ) which depends on ||c 0 ||, α and T :…”

Section: Non-conservative Truncation and Required Resultsmentioning

confidence: 99%

Section: Conservative Truncation and Required Resultsmentioning

confidence: 99%

Section: Prologuementioning

confidence: 99%

Section: Existing Literaturementioning

confidence: 99%

Section: Existing Literaturementioning

confidence: 99%

See 3 more Smart Citations

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Kaushik¹,

Kumar²

2022

Preprint

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Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models

Kushwah

Saha

2022

Math Methods in App Sciences

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We discuss the formulation of a numerical scheme based on the homotopy method to solve different aggregation–fragmentation models including the simultaneous event. Several test cases are considered and analyzed qualitatively and quantitatively to ascertain the improved accuracy and efficiency of the proposed model over the existing semi‐analytical models. The generalized solution of the truncated problem is obtained for some test cases, which in the limiting sense tends to the exact solution. A detailed convergence analysis of the scheme is also studied.

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

Ali,

Rai,

Giri

2023

Math Methods in App Sciences

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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.

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Structural stability of disperse systems and finite nature of a coagulation front

Cited by 14 publications

References 12 publications

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models

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

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