Abstract
We develop techniques for estimating the coefficients, boundary data, and initial data associated with transport equations (or more generally, parabolic distributed models). Our estimation schemes are based on cubic spline approximations, for which convergence results are given. We discuss the performance of these techniques in two investigations of biological interest: (1) transport of labeled sucrose in brain tissue white matter, (2) insect dispersal that cannot be modeled by a random diffusion mechanism alone.
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This research has been supported in part by the Air Force Office of Scientific Research under contract # AF-AFOSR # 81-0198, in part by the National Science Foundation under contract # MCS 79-05774-05, and in part by the U.S. Army Research Office under contract # ARO-DAAG-29-79-C-0161
Collection of data concerning beetle dispersal was supported by NSF grant DEB 77-25120 to Richard B. Root. Subsequent computer analyses of these dispersal data were supported in part by NSF grant DEB 8207117 to P. Kareiva
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Banks, H.T., Kareiva, P. Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models. J. Math. Biology 17, 253–273 (1983). https://doi.org/10.1007/BF00276516
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DOI: https://doi.org/10.1007/BF00276516