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Local well posedness for a linear coagulation equation

Authors: M. Escobedo and J. J. L. Velázquez
Journal: Trans. Amer. Math. Soc. 365 (2013), 1743-1808
MSC (2010): Primary 45K05, 45A05, 45M05, 82C40, 82C05, 82C22
Published electronically: October 4, 2012
MathSciNet review: 3009645
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Abstract: In this paper a family of linear coagulation models is solved. These models arise in the analysis of the asymptotic behaviour of coagulation equations yielding gelation for large particles. The tools and techniques that are developed in this paper are based on the definition of a class of weighted Sobolev spaces that take into account the characteristic time scales associated to the coagulation equation for large particles, as well as in the continuation argument introduced by Schauder to prove well posedness of general classes of elliptic and parabolic equations.

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Additional Information

M. Escobedo
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E–48080 Bilbao, Spain

J. J. L. Velázquez
Affiliation: ICMAT (CSIC-UAM-UC3M-UCM) Facultad de Matemáticas, Universidad Complutense, E–28040 Madrid, Spain
Address at time of publication: Institute of Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Email: JJ{\textunderscore}, velazquez@iam.uni{\textunderscore}

Received by editor(s): August 3, 2010
Received by editor(s) in revised form: February 23, 2011
Published electronically: October 4, 2012
Article copyright: © Copyright 2012 American Mathematical Society