Well-posedness of the discrete collision-induced breakage equation with unbounded fragmentation distribution - Université Savoie Mont Blanc Access content directly
Journal Articles Nonlinear Analysis: Real World Applications Year : 2024

Well-posedness of the discrete collision-induced breakage equation with unbounded fragmentation distribution

Mashkoor Ali
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  • PersonId : 1220344
Ankik Kumar Giri
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  • PersonId : 1073218
Philippe Laurençot

Abstract

A discrete version of the nonlinear collision-induced breakage equation is studied. Existence of solutions is investigated for a broad class of unbounded collision kernels and daughter distribution functions, the collision kernel $a_{i,j}$ satisfiying $a_{i,j} \leq A i j$ for some $A>0$. More precisely, it is proved that, given suitable conditions, there exists at least one mass-conserving solution for all times. A result on the uniqueness of solutions is also demonstrated under reasonably general conditions. Furthermore, the propagation of moments, differentiability, and the continuous dependence of solutions are established, along with some invariance properties and the large-time behaviour of solutions.
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Dates and versions

hal-03958853 , version 1 (26-01-2023)

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Mashkoor Ali, Ankik Kumar Giri, Philippe Laurençot. Well-posedness of the discrete collision-induced breakage equation with unbounded fragmentation distribution. Nonlinear Analysis: Real World Applications, 2024, 75, pp.103967. ⟨hal-03958853⟩
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