Differential and Integral Equations

Well-posedness for a coagulation multiple-fragmentation equation

Eduardo Cepeda

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Abstract

We consider a coagulation multiple-fragmentation equation, which describes the concentration $c_t(x)$ of particles of mass $x \in (0,\infty)$ at the instant $t \geq 0$ in a model where fragmentation and coalescence phenomena occur. We study the existence and uniqueness of measured-valued solutions to this equation for homogeneous-like kernels of homogeneity parameter $\lambda \in (0,1]$ and bounded fragmentation kernels, although a possibly infinite total fragmentation rate, in particular an infinite number of fragments, is considered. This work relies on the use of a Wasserstein-type distance, which has shown to be particularly well-adapted to coalescence phenomena. It was introduced in previous works on coagulation and coalescence.

Article information

Source
Differential Integral Equations, Volume 27, Number 1/2 (2014), 105-136.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1384282856

Mathematical Reviews number (MathSciNet)
MR3161598

Zentralblatt MATH identifier
1313.45011

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]

Citation

Cepeda, Eduardo. Well-posedness for a coagulation multiple-fragmentation equation. Differential Integral Equations 27 (2014), no. 1/2, 105--136. https://projecteuclid.org/euclid.die/1384282856


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