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An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume
1.  School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009 
2.  Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA 6846, Australia 
[1] 
Shalela Mohd Mahali, Song Wang, Xia Lou. Determination of effective diffusion coefficients of drug delivery devices by a state observer approach. Discrete & Continuous Dynamical Systems  B, 2011, 16 (4) : 11191136. doi: 10.3934/dcdsb.2011.16.1119 
[2] 
Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reactiondiffusion patterns. Communications on Pure & Applied Analysis, 2012, 11 (1) : 189207. doi: 10.3934/cpaa.2012.11.189 
[3] 
Shalela MohdMahali, Song Wang, Xia Lou, Sungging Pintowantoro. Numerical methods for estimating effective diffusion coefficients of threedimensional drug delivery systems. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 377393. doi: 10.3934/naco.2012.2.377 
[4] 
Xin Li, Xingfu Zou. On a reactiondiffusion model for sterile insect release method with release on the boundary. Discrete & Continuous Dynamical Systems  B, 2012, 17 (7) : 25092522. doi: 10.3934/dcdsb.2012.17.2509 
[5] 
Zhidong Zhang. An undetermined timedependent coefficient in a fractional diffusion equation. Inverse Problems & Imaging, 2017, 11 (5) : 875900. doi: 10.3934/ipi.2017041 
[6] 
Elena Beretta, Cecilia Cavaterra. Identifying a space dependent coefficient in a reactiondiffusion equation. Inverse Problems & Imaging, 2011, 5 (2) : 285296. doi: 10.3934/ipi.2011.5.285 
[7] 
Giovany M. Figueiredo, Tarcyana S. FigueiredoSousa, Cristian MoralesRodrigo, Antonio Suárez. Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 36893711. doi: 10.3934/dcdsb.2018311 
[8] 
Zhi Lin, Katarína Boďová, Charles R. Doering. Models & measures of mixing & effective diffusion. Discrete & Continuous Dynamical Systems  A, 2010, 28 (1) : 259274. doi: 10.3934/dcds.2010.28.259 
[9] 
ZhiXue Zhao, Mapundi K. Banda, BaoZhu Guo. Boundary switch on/off control approach to simultaneous identification of diffusion coefficient and initial state for onedimensional heat equation. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 00. doi: 10.3934/dcdsb.2020021 
[10] 
Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami Radunskaya, Ian Tucker. Predicting the drug release kinetics of matrix tablets. Discrete & Continuous Dynamical Systems  B, 2009, 12 (2) : 261277. doi: 10.3934/dcdsb.2009.12.261 
[11] 
Vladimir V. Chepyzhov, Mark I. Vishik. Trajectory attractor for reactiondiffusion system with diffusion coefficient vanishing in time. Discrete & Continuous Dynamical Systems  A, 2010, 27 (4) : 14931509. doi: 10.3934/dcds.2010.27.1493 
[12] 
Zhenzhen Chen, SzeBi Hsu, YaTang Yang. The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants. Communications on Pure & Applied Analysis, 2020, 19 (1) : 203220. doi: 10.3934/cpaa.2020011 
[13] 
Nicolas Bacaër, Cheikh Sokhna. A reactiondiffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227238. doi: 10.3934/mbe.2005.2.227 
[14] 
Bastian Harrach. Simultaneous determination of the diffusion and absorption coefficient from boundary data. Inverse Problems & Imaging, 2012, 6 (4) : 663679. doi: 10.3934/ipi.2012.6.663 
[15] 
Yunmei Chen, Weihong Guo, Qingguo Zeng, Yijun Liu. A nonstandard smoothing in reconstruction of apparent diffusion coefficient profiles from diffusion weighted images. Inverse Problems & Imaging, 2008, 2 (2) : 205224. doi: 10.3934/ipi.2008.2.205 
[16] 
Elie Bretin, Imen Mekkaoui, Jérôme Pousin. Assessment of the effect of tissue motion in diffusion MRI: Derivation of new apparent diffusion coefficient formula. Inverse Problems & Imaging, 2018, 12 (1) : 125152. doi: 10.3934/ipi.2018005 
[17] 
Thuy N. T. Nguyen. Carleman estimates for semidiscrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability. Mathematical Control & Related Fields, 2014, 4 (2) : 203259. doi: 10.3934/mcrf.2014.4.203 
[18] 
M. Grasselli, V. Pata. A reactiondiffusion equation with memory. Discrete & Continuous Dynamical Systems  A, 2006, 15 (4) : 10791088. doi: 10.3934/dcds.2006.15.1079 
[19] 
Kin Ming Hui. Collasping behaviour of a singular diffusion equation. Discrete & Continuous Dynamical Systems  A, 2012, 32 (6) : 21652185. doi: 10.3934/dcds.2012.32.2165 
[20] 
Claude Bardos, François Golse, Ivan Moyano. Linear Boltzmann equation and fractional diffusion. Kinetic & Related Models, 2018, 11 (4) : 10111036. doi: 10.3934/krm.2018039 
2018 Impact Factor: 1.025
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