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<p>We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove existence, uniqueness and positivity of solutions of a corresponding semi-linear Cauchy problem in a weighted <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ell ^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> space. This requires the application of novel results, which we prove for abstract semi-linear Cauchy problems in Banach lattices where the non-linear term is defined only on a dense subspace.</p>

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Discrete Coagulation–Fragmentation Systems in Weighted \(\ell ^1\) Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月20日

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  • Lyndsay Kerr,
  • Matthias Langer

摘要

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove existence, uniqueness and positivity of solutions of a corresponding semi-linear Cauchy problem in a weighted \(\ell ^1\) ℓ 1 space. This requires the application of novel results, which we prove for abstract semi-linear Cauchy problems in Banach lattices where the non-linear term is defined only on a dense subspace.