Mathematical Biosciences and Engineering, 2019, 16(6): 6728-6752. doi: 10.3934/mbe.2019336

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Mathematical modeling and analysis of harmful algal blooms in flowing habitats

Sze-Bi Hsu, Feng-Bin Wang, Xiao-Qiang Zhao

1 Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan
2 Department of Natural Science in the Center for General Education, Chang Gung University, Guishan, Taoyuan 333, Taiwan; and Community Medicine Research Center, Chang Gung Memorial Hospital, Keelung branch, Keelung 204, Taiwan
3 Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada

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Special Issues: Recent Advances in Mathematical Population Dynamics

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In this paper, we survey recent developments of mathematical modeling and analysis of the dynamics of harmful algae in riverine reservoirs. To make the models more realistic, a hydraulic storage zone is incorporated into a flow reactor model and new mathematical challenges arise from the loss of compactness of the solution maps. The key point in the study of the evolution dynamics is to prove the existence of global attractors for the model systems and the principal eigenvalues for the associated linearized systems without compactness.
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