Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Lipschitz semigroup for an integro-differential equation for slow erosion

Authors: Rinaldo M. Colombo, Graziano Guerra and Wen Shen
Journal: Quart. Appl. Math. 70 (2012), 539-578
MSC (2010): Primary 35L65; Secondary 35L67, 35Q70, 35L60, 35L03
DOI: https://doi.org/10.1090/S0033-569X-2012-01309-2
Published electronically: May 18, 2012
MathSciNet review: 2986134
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Abstract: In this paper we study an integro-differential equation describing granular flow dynamics with slow erosion. This nonlinear partial differential equation is a conservation law where the flux contains an integral term. Through a generalized wave front tracking algorithm, approximate solutions are constructed and shown to converge strongly to a Lipschitz semigroup.

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Additional Information

Rinaldo M. Colombo
Affiliation: Department of Mathematics, Brescia University, Italy
Email: rinaldo.colombo@unibs.it

Graziano Guerra
Affiliation: Department of Mathematics and Applications, Milano-Bicocca University, Italy
Email: graziano.guerra@unimib.it

Wen Shen
Affiliation: Department of Mathematics, Penn State University, Altoona, Pennsylvania 16601
Email: shen{\textunderscore}w@math.psu.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01309-2
Received by editor(s): December 22, 2011
Published electronically: May 18, 2012
Additional Notes: The work of this author was partially supported by an NSF grant no DMS-0908047.
Dedicated: Dedicated to Constantine Dafermos in honor of his 70th Birthday
Article copyright: © Copyright 2012 Brown University

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