Well-posedness for boundary value problems for coagulation-fragmentation equations

Iñigo U. Erneta

doi:10.3934/krm.2020028

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2020, Volume 13, Issue 4: 815-835. Doi: 10.3934/krm.2020028

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Well-posedness for boundary value problems for coagulation-fragmentation equations

Iñigo U. Erneta

Universitat Politècnica de Catalunya - BGSMath, Departament de Matemàtiques, Av. Diagonal 647, 08028 Barcelona, Spain

Received: October 2019

Revised: January 2020

Published: May 2020

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Abstract

We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zero and showing existence of solutions for the singular kernels relevant in the applications. We determine the large time asymptotic behavior of solutions, proving that solutions converge exponentially fast to zero in the absence of fragmentation and stabilize toward an equilibrium if the boundary value satisfies a detailed balance condition. Incidentally, we obtain an improvement in the regularity of solutions by showing the finiteness of negative moments for positive time.

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Mathematics Subject Classification: 35A01, 35R09.

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