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Applicable Analysis
An International Journal
Volume 19, 1985 - Issue 2-3
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Original Articles

The Solution of an Evolution Equation Describing Certain Types of Mechanical and Chemical Interaction

Pages 75-88 | Published online: 02 May 2007
 

Abstract

AMS (MOS): 45K05, 45G10

Consider the initial value problem (∗) where A is a certain quadratic integral operator which does not depend on t explicitly. The equation describes the evolution in time of the volume distribution, u , of an ensemble of particles undergoing concurrent coalescence and fracture. It is shown (∗) has a unique solution valid for all t⩾0 in the Banach spaces and X , the space of bounded Lebesgue measurable functions on [0, V0] V0 is the total ensemble volume. The solution satisfies u ⩾0 for all (or almost all) conserves total volume and depends continuously on u0. While in general equations like (∗) do not possess solutions valid for all t ⩾ 0 , (∗) does precisely because of the non-negativity and volume conservation. The proof exploits an interesting inter-play between the two spaces. Both spaces must be considered to get the solution in either one.

Additional information

Notes on contributors

W. Walter

Kenneth L. Kuttler

John W Hilgers

Thomas H Courtney

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