Local well posedness for a linear coagulation equation
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- by M. Escobedo and J. J. L. Velázquez PDF
- Trans. Amer. Math. Soc. 365 (2013), 1743-1808 Request permission
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.References
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Additional Information
- M. Escobedo
- Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E–48080 Bilbao, Spain
- Email: mtpesmam@lg.ehu.es
- 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
- MR Author ID: 289301
- Email: JJ_Velazquez@mat.ucm.es, velazquez@iam.uni_bonn.de
- Received by editor(s): August 3, 2010
- Received by editor(s) in revised form: February 23, 2011
- Published electronically: October 4, 2012
- © Copyright 2012 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 1743-1808
- MSC (2010): Primary 45K05, 45A05, 45M05, 82C40, 82C05, 82C22
- DOI: https://doi.org/10.1090/S0002-9947-2012-05576-0
- MathSciNet review: 3009645