The Continuous Coagulation-Fragmentation¶Equations with Diffusion

Laurençot, Philippe; Mischler, Stéphane

doi:10.1007/s002050100186

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Introduction3

Asymptotic Behaviour Of Liquid-liquid Dispersions1

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2004

2022

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Cited by 72 publications

(49 citation statements)

References 28 publications

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“…We mention polymerization and depolimerization phenomena in chemical engineering, agglutination and splitting of blood cells, formation and splitting of aerosol droplets or evolution of phytoplankton aggregates as some of the recently analyzed cases, see e.g. [1,2,9,13]. Fragmentation and coagulation processes, modeled here by integral operators, often are accompanied by growth or decay of aggregates e.g.…”

Section: Introductionmentioning

confidence: 99%

Global Solvability of a Fragmentation-Coagulation Equation With Growth and Restricted Coagulation

Banasiak¹,

Noutchie²,

Rudnicki³

2021

JNMP

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Section: Introductionmentioning

confidence: 99%

Global Solvability of a Fragmentation-Coagulation Equation With Growth and Restricted Coagulation

Banasiak¹,

Noutchie²,

Rudnicki³

2021

JNMP

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“…in the kinetic theory of polymers [21]; see also [2,3,18]; and coagulationfragmentation problems [17]), molecular biology [10], and mathematical finance. Important special cases of these equations include the following:…”

mentioning

confidence: 99%

Sparse finite element approximation of high-dimensional transport-dominated diffusion problems

Schwab¹,

Süli

Todor³

2008

ESAIM: M2AN

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Abstract.We develop the analysis of stabilized sparse tensor-product finite element methods for high-dimensional, non-self-adjoint and possibly degenerate second-order partial differential equations of the form −a :where a ∈ R d×d is a symmetric positive semidefinite matrix, using piecewise polynomials of degree p ≥ 1. Our convergence analysis is based on new high-dimensional approximation results in sparse tensor-product spaces. We show that the error between the analytical solution u and its stabilized sparse finite element approximation u h on a partition of Ω of mesh size h = hL = 2 −L satisfies the following bound in the streamline-diffusion norm ||| · |||SD, provided u belongs to the space H k+1 (Ω) of functions with square-integrable mixed (k + 1)st derivatives: Mathematics Subject Classification. 65N30. Received March 7, 2007. Received February 11, 2008. Published online July 30, 2008 Dedicated to Henryk Woźniakowski, on the occasion of his 60th birthday.

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“…For related recent work see Amann [1] and Laurençot and Mischler [4], [5]. Full details of the results presented in this paper will appear elsewhere.…”

Section: Introductionmentioning

confidence: 89%