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dc.contributor.authorHaskovec, Jan
dc.contributor.authorOlez, Dietmar
dc.date.accessioned2021-07-05T07:57:34Z
dc.date.available2021-07-05T07:57:34Z
dc.date.issued2015
dc.date.submitted2014-01
dc.identifier.citationHaškovec, J., & Oelz, D. (2015). A free boundary problem for aggregation by short range sensing and differentiated diffusion. Discrete and Continuous Dynamical Systems - Series B, 20(5), 1461–1480. doi:10.3934/dcdsb.2015.20.1461
dc.identifier.issn1553-524X
dc.identifier.issn1531-3492
dc.identifier.doi10.3934/dcdsb.2015.20.1461
dc.identifier.urihttp://hdl.handle.net/10754/670004
dc.description.abstractOn the d-dimensional torus we consider the drift-diffusion equation, where the diffusion coefficient may take one of two possible values depending on whether the locally sensed density is below or above a given threshold. This can be interpreted as an aggregation model for particles like insect populations or freely diffusing proteins which slow down their dynamics within dense aggregates. This leads to a free boundary model where the free boundary separates densely packed aggregates from areas with a loose particle concentration. The paper has a rigorous part and a formal part. In the rigorous part we prove existence of solutions to the distributional formulation of the model. In the second, formal, part we derive the strong formulation of the model including the free boundary conditions and characterize stationary solutions giving necessary conditions for the emergence of stationary plateaus. We conclude that stationary aggregation plateaus in this situation are either spherical, complements of sphericals or stripes, which has implications for biological applications. Finally, numerical simulations in one and two dimensions are used to give evidence for the long time convergence to stationary states which feature aggregations.
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.urlhttp://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11122
dc.rightsThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B following peer review. The definitive publisher-authenticated version is available online at: http://doi.org/10.3934/dcdsb.2015.20.1461
dc.subjectParabolic equation with discontinuous coefficients
dc.subjectpiecewise constant volatility
dc.subjectaggregation
dc.subjectdifferentiated diffusion
dc.subjectparabolic free boundary problem
dc.titleA FREE BOUNDARY PROBLEM FOR AGGREGATION BY SHORT RANGE SENSING AND DIFFERENTIATED DIFFUSION
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series B
dc.identifier.wosutWOS:000355570400011
dc.eprint.versionPost-print
dc.contributor.institutionCourant Institute of Mathematical Sciences, New York University (NYU), 251 Mercer Street, New York, NY, 10012-1185, United States
dc.identifier.volume20
dc.identifier.issue5
dc.identifier.pages1461-1480
kaust.personHaskovec, Jan
dc.date.accepted2014-11
dc.identifier.eid2-s2.0-84946154578


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