2016, 13(5): 911-934. doi: 10.3934/mbe.2016023

Using drinking data and pharmacokinetic modeling to calibrate transport model and blind deconvolution based data analysis software for transdermal alcohol biosensors

1. 

Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, United States, United States, United States

2. 

School of Public Health, Brown University, Providence, RI 02912, United States

3. 

Department of Psychology, University of Southern California, Los Angeles, CA 90089-1061, United States

Received  September 2015 Revised  April 2016 Published  July 2016

Alcohol researchers/clinicians have two ways to collect subject /patient field data, standard-drink self-report and the breath analyzer, neither of which is passive or accurate because active subject participation is required. Transdermal alcohol sensors have been developed to measure transdermal alcohol concentration (TAC), but they are used primarily as abstinence monitors because converting TAC into more meaningful blood/breath alcohol concentration (BAC/BrAC) is difficult. In this paper, BAC/BrAC is estimated from TAC by first calibrating forward distributed parameter-based convolution models for ethanol transport from the blood through the skin using patient-collected drinking data for a single drinking episode and a nonlinear pharmacokinetic metabolic absorption/elimination model to estimate BAC. TAC and estimated BAC are then used to fit the forward convolution filter. Nonlinear least squares with adjoint-based gradient computation are used to fit both models. Calibration results are compared with those obtained using BAC/BrAC from alcohol challenges and from standard, linear, metabolic absorption, and zero order kinetics-based elimination models, by considering peak BAC, time of peak, and area under the BAC curve. Our models (with population parameters) could be included in a smart phone app that makes it convenient for the subject/patient to enter drinking data for a single episode in the field.
Citation: Zheng Dai, I.G. Rosen, Chuming Wang, Nancy Barnett, Susan E. Luczak. Using drinking data and pharmacokinetic modeling to calibrate transport model and blind deconvolution based data analysis software for transdermal alcohol biosensors. Mathematical Biosciences & Engineering, 2016, 13 (5) : 911-934. doi: 10.3934/mbe.2016023
References:
[1]

R. A. Adams, Sobolev Spaces,, Academic Press, (1975).   Google Scholar

[2]

J. C. Anderson and M. P. Hlastala, The kinetics of transdermal ethanol exchange,, Journal of Applied Physiology, 100 (2006), 649.   Google Scholar

[3]

H. T. Banks and K. Ito, A unified framework for approximation in inverse problems for distributed parameter systems,, Control Theory and Advanced Technology, 4 (1988), 73.   Google Scholar

[4]

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems,, Birkhauser, (1989).  doi: 10.1007/978-1-4612-3700-6.  Google Scholar

[5]

H. T. Banks and K. Ito, Approximation in LQR problems for infinite dimensional systems with unbounded input operators,, J. Mathematical Systems, 7 (1997), 1.   Google Scholar

[6]

D. P. Bertsekas, Nonlinear Programming (2nd ed.),, Athena Scientific, (1999).   Google Scholar

[7]

S. P. Bradley, A. C. Hax and T. L. Magnanti, Applied Mathematical Programming,, Addison-Wesley, (1977).   Google Scholar

[8]

K. B. Carey and J. T. P. Hustad, Are retrospectively reconstructed blood alcohol concentrations accurate?, Preliminary results from a field study,, Journal of Studies on Alcohol, 63 (2002), 762.   Google Scholar

[9]

C.-T. Chen, Linear System Theory and Design,, Holt Rinehart and Winston, (1970).   Google Scholar

[10]

R. F. Curtain and D. Salamon, Finite dimensional compensators and infinite dimensional systems with unbounded input operators,, SIAM J. Control and Optimization, 24 (1986), 797.  doi: 10.1137/0324050.  Google Scholar

[11]

D. M. Dougherty, N. E. Charles, A. Acheson, S. John, R. M. Furr and N. Hill-Kapturczak, Comparing the detection of transdermal and breath alcohol concentrations during periods of alcohol consumption ranging from moderate drinking to binge drinking,, Exp Clin Psychopharm, 203 (2012), 73.   Google Scholar

[12]

M. Dumett, I. G. Rosen, J. Sabat, A. Shaman, L. A. Tempelman, C. Wang and R. M. Swift, Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data,, Applied Mathematics and Computation, 196 (2008), 724.  doi: 10.1016/j.amc.2007.07.026.  Google Scholar

[13]

L. Edelstein-Keshet, Mathematical Models in Biology,, Society for Industrial and Applied Mathematics, (2005).  doi: 10.1137/1.9780898719147.  Google Scholar

[14]

A. R. W. Forrest, The estimation of Widmark's factor,, Journal of the Forensic Science Society, 26 (1986), 249.   Google Scholar

[15]

J. S. Gibson and I. G. Rosen, Approximation of discrete time LQG compensators for distributed systems with boundary input and unbounded measurement,, Automatica, 24 (1988), 517.  doi: 10.1016/0005-1098(88)90096-9.  Google Scholar

[16]

A. Heck, Modeling intake and clearance of alcohol in humans,, The Electronic Journal of Mathematics and Technology, 1 (2007), 232.   Google Scholar

[17]

N. Hill-Kapturczak, S. L. Lake, J. D. Roache, S. E. Cates, Y. Liang and D. M. Dougherty, Do variable rates of alcohol drinking alter the ability to use transdermal alcohol monitors to estimate peak, breath alcohol and total number of drinks?,, ACER, 38 (2014), 2517.  doi: 10.1111/acer.12528.  Google Scholar

[18]

N. Hill-Kapturczak, J. D. Roache, Y. Liang, T. E. Karns, S. E. Cates and D. M. Dougherty, Accounting for sex-related differences in the estimation of breath alcohol concentrations using transdermal alcohol monitoring,, Psychopharmacology , 232 (2015), 115.  doi: 10.1007/s00213-014-3644-9.  Google Scholar

[19]

N. Hill-Kapturczak, J. D. Roache, C. J. Walters, T. E. Karns, S. E. Cates and D. M. Dougherty, Validation of using transdermal alcohol concentrations to estimate breath alcohol,, ACER., ().   Google Scholar

[20]

E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups,, American Mathematical Society, (1957).   Google Scholar

[21]

J. T. P. Hustad and K. B. Carey, Using calculations to estimate blood alcohol concentrations for naturally occurring drinking episodes: A validity study,, Journal of Studies on Alcohol, 66 (2005), 130.   Google Scholar

[22]

T. Kato, Perturbation Theory for Linear Operators,, Second Edition, (1976).   Google Scholar

[23]

D. A. Labianca, The chemical basis of the breathalyzer,a critical analysis,, Journal of Chemical Education, 67 (1990), 259.   Google Scholar

[24]

A. J. Levi and I. G. Rosen, A novel formulation of the adjoint method in the optimal design of quantum electronic devices,, Siam Journal on Control and Optimization, 48 (2010), 3191.  doi: 10.1137/070708330.  Google Scholar

[25]

M. J. Lewis, The individual and the estimation of his blood alcohol concentration from intake, with particular reference to the "hip-flask" drink,, Journal of the Forensic Science Society, 26 (1986), 19.   Google Scholar

[26]

L. Li and T. P. Speed, Parametric deconvolution of positive spike trains,, Annals of Statistics, 28 (2000), 1279.  doi: 10.1214/aos/1015957394.  Google Scholar

[27]

J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations,, Springer-Verlag, (1971).   Google Scholar

[28]

S. E. Luczak, I. G. Rosen and T. L. Wall, Development of a real-time repeated-measures assessment protocol to capture change over the course of a drinking episode,, Alcohol and Alcoholism, 50 (2015), 1.   Google Scholar

[29]

S. E. Luczak, I. G. Rosen and J. Weiss, Determining blood and/or breath alcohol concentration from transdermal alcohol data, Proceedings of the 2013 American control conference,, International Federation of Automatic Control, (2013), 473.   Google Scholar

[30]

P. R. Marques and A. S. McKnight, Field and laboratory alcohol detection with 2 types of transdermal devices,, Alcohol Clin Exp Res, 33 (2009), 703.   Google Scholar

[31]

D. B. Matthews and W. R. Miller, Estimating blood alcohol concentration: Two computer programs and their applications in therapy and research,, Addictive Behaviors, 4 (1979), 55.   Google Scholar

[32]

I. Najfeld and T. F. Havel, Derivatives of the matrix exponential,, Advances in Applied Mathematics, 16 (1995), 321.  doi: 10.1006/aama.1995.1017.  Google Scholar

[33]

National Highway Traffic Safety Administration, Computing a BAC Estimate,, Department of Transportation, (1994).   Google Scholar

[34]

A. Okubo, Diffusion and Ecological Problems: Mathematical Models,, Springer-Verlag, (1980).   Google Scholar

[35]

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer-Verlag, (1983).  doi: 10.1007/978-1-4612-5561-1.  Google Scholar

[36]

A. J. Pritchard and D. Salamon, The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators,, SIAM J. Control and Optimization, 25 (1987), 121.  doi: 10.1137/0325009.  Google Scholar

[37]

I. G. Rosen, S. E. Luczak and J. Weiss, Blind deconvolution for distributed parameter systems with unbounded input and output and determining blood alcohol concentration from transdermal biosensor data,, Applied Math and Computation, 231 (2014), 357.  doi: 10.1016/j.amc.2013.12.099.  Google Scholar

[38]

I. G. Rosen, S. E. Luczak, W. Hu and M. Hankin, Discrete-time blind deconvolution for distributed parameter systems with Dirichlet boundary input and unbounded output with application to a transdermal alcohol biosensor,, Proceedings of 2013 SIAM Conference on Control and its Applications, (2013).   Google Scholar

[39]

J. T. Sakai, S. K. Mikulich-Gilbertson, R. J. Long and T. J. Crowley, Validity of transdermal alcohol monitoring: Fixed and self-regulated dosing,, Alcohol Clin Exp Res, 30 (2006), 26.   Google Scholar

[40]

M. Schultz, Spline Analysis,, Prentice Hall, (1973).   Google Scholar

[41]

R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,, London, (1977).   Google Scholar

[42]

L. C. Sobell and M. C. Sobell, Alcohol time-Line follow-back: A technique for assessing self-reported alcohol consumption, In R. Z. Litten and J. P. Allens (Eds.), Measuring Alcohol Consumption,, Humana Press, (1992).   Google Scholar

[43]

O. J. Staffans, Well-Posed Linear Systems,, Cambridge University Press, (2005).  doi: 10.1017/CBO9780511543197.  Google Scholar

[44]

R. M. Swift, Direct measurement of alcohol and its metabolites,, Addiction, 98S (2003), 78.   Google Scholar

[45]

R. M. Swift and L. L. Swette, Assessment of ethanol consumption with a wearable, electronic ethanol sensor/recorder, In R. Litten, and J. Allen (Eds.), Measuring Alcohol Consumption: Psychosocial and biological methods,, Humana Press, (1992).   Google Scholar

[46]

H. Tanabe, Equations of Evolution,, Pitman, (1979).   Google Scholar

[47]

M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups,, Birkhauser, (2009).  doi: 10.1007/978-3-7643-8994-9.  Google Scholar

[48]

J. G. Wagner and J. A. Patel, Variations in absorption and elimination rates of ethyl alcohol in a single subject,, Research Communications in Chemical Pathology and Pharmacology, 4 (1972), 61.   Google Scholar

[49]

P. E. Watson, I. D. Watson and R. D. Batt, Total body water volumes for adult males and females estimated from simple anthropometric measurements,, American Journal of Clinical Nutrition, 33 (1980), 27.   Google Scholar

[50]

P. E. Watson, I. D. Watson and R. D. Batt, Prediction of blood alcohol concentrations in human subjects: Updating the Widmark equation,, Journal of Studies on Alcohol, 42 (1981), 547.   Google Scholar

[51]

G. D. Webster and H. C. Gabler, Feasibility of transdermal ethanol sensing for the detection of intoxicated drivers,, Annu Proc Assoc Adv Automot Med, 51 (2007), 449.   Google Scholar

[52]

G. D. Webster and H. C. Gabler, Modeling of transdermal transport of alcohol: effect of body mass and gender,, Biomedical Sciences Instrumentation, 44 (2007), 361.   Google Scholar

[53]

J. Wloka, Partial Differential Equations,, Cambridge University Press, (1987).  doi: 10.1017/CBO9781139171755.  Google Scholar

show all references

References:
[1]

R. A. Adams, Sobolev Spaces,, Academic Press, (1975).   Google Scholar

[2]

J. C. Anderson and M. P. Hlastala, The kinetics of transdermal ethanol exchange,, Journal of Applied Physiology, 100 (2006), 649.   Google Scholar

[3]

H. T. Banks and K. Ito, A unified framework for approximation in inverse problems for distributed parameter systems,, Control Theory and Advanced Technology, 4 (1988), 73.   Google Scholar

[4]

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems,, Birkhauser, (1989).  doi: 10.1007/978-1-4612-3700-6.  Google Scholar

[5]

H. T. Banks and K. Ito, Approximation in LQR problems for infinite dimensional systems with unbounded input operators,, J. Mathematical Systems, 7 (1997), 1.   Google Scholar

[6]

D. P. Bertsekas, Nonlinear Programming (2nd ed.),, Athena Scientific, (1999).   Google Scholar

[7]

S. P. Bradley, A. C. Hax and T. L. Magnanti, Applied Mathematical Programming,, Addison-Wesley, (1977).   Google Scholar

[8]

K. B. Carey and J. T. P. Hustad, Are retrospectively reconstructed blood alcohol concentrations accurate?, Preliminary results from a field study,, Journal of Studies on Alcohol, 63 (2002), 762.   Google Scholar

[9]

C.-T. Chen, Linear System Theory and Design,, Holt Rinehart and Winston, (1970).   Google Scholar

[10]

R. F. Curtain and D. Salamon, Finite dimensional compensators and infinite dimensional systems with unbounded input operators,, SIAM J. Control and Optimization, 24 (1986), 797.  doi: 10.1137/0324050.  Google Scholar

[11]

D. M. Dougherty, N. E. Charles, A. Acheson, S. John, R. M. Furr and N. Hill-Kapturczak, Comparing the detection of transdermal and breath alcohol concentrations during periods of alcohol consumption ranging from moderate drinking to binge drinking,, Exp Clin Psychopharm, 203 (2012), 73.   Google Scholar

[12]

M. Dumett, I. G. Rosen, J. Sabat, A. Shaman, L. A. Tempelman, C. Wang and R. M. Swift, Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data,, Applied Mathematics and Computation, 196 (2008), 724.  doi: 10.1016/j.amc.2007.07.026.  Google Scholar

[13]

L. Edelstein-Keshet, Mathematical Models in Biology,, Society for Industrial and Applied Mathematics, (2005).  doi: 10.1137/1.9780898719147.  Google Scholar

[14]

A. R. W. Forrest, The estimation of Widmark's factor,, Journal of the Forensic Science Society, 26 (1986), 249.   Google Scholar

[15]

J. S. Gibson and I. G. Rosen, Approximation of discrete time LQG compensators for distributed systems with boundary input and unbounded measurement,, Automatica, 24 (1988), 517.  doi: 10.1016/0005-1098(88)90096-9.  Google Scholar

[16]

A. Heck, Modeling intake and clearance of alcohol in humans,, The Electronic Journal of Mathematics and Technology, 1 (2007), 232.   Google Scholar

[17]

N. Hill-Kapturczak, S. L. Lake, J. D. Roache, S. E. Cates, Y. Liang and D. M. Dougherty, Do variable rates of alcohol drinking alter the ability to use transdermal alcohol monitors to estimate peak, breath alcohol and total number of drinks?,, ACER, 38 (2014), 2517.  doi: 10.1111/acer.12528.  Google Scholar

[18]

N. Hill-Kapturczak, J. D. Roache, Y. Liang, T. E. Karns, S. E. Cates and D. M. Dougherty, Accounting for sex-related differences in the estimation of breath alcohol concentrations using transdermal alcohol monitoring,, Psychopharmacology , 232 (2015), 115.  doi: 10.1007/s00213-014-3644-9.  Google Scholar

[19]

N. Hill-Kapturczak, J. D. Roache, C. J. Walters, T. E. Karns, S. E. Cates and D. M. Dougherty, Validation of using transdermal alcohol concentrations to estimate breath alcohol,, ACER., ().   Google Scholar

[20]

E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups,, American Mathematical Society, (1957).   Google Scholar

[21]

J. T. P. Hustad and K. B. Carey, Using calculations to estimate blood alcohol concentrations for naturally occurring drinking episodes: A validity study,, Journal of Studies on Alcohol, 66 (2005), 130.   Google Scholar

[22]

T. Kato, Perturbation Theory for Linear Operators,, Second Edition, (1976).   Google Scholar

[23]

D. A. Labianca, The chemical basis of the breathalyzer,a critical analysis,, Journal of Chemical Education, 67 (1990), 259.   Google Scholar

[24]

A. J. Levi and I. G. Rosen, A novel formulation of the adjoint method in the optimal design of quantum electronic devices,, Siam Journal on Control and Optimization, 48 (2010), 3191.  doi: 10.1137/070708330.  Google Scholar

[25]

M. J. Lewis, The individual and the estimation of his blood alcohol concentration from intake, with particular reference to the "hip-flask" drink,, Journal of the Forensic Science Society, 26 (1986), 19.   Google Scholar

[26]

L. Li and T. P. Speed, Parametric deconvolution of positive spike trains,, Annals of Statistics, 28 (2000), 1279.  doi: 10.1214/aos/1015957394.  Google Scholar

[27]

J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations,, Springer-Verlag, (1971).   Google Scholar

[28]

S. E. Luczak, I. G. Rosen and T. L. Wall, Development of a real-time repeated-measures assessment protocol to capture change over the course of a drinking episode,, Alcohol and Alcoholism, 50 (2015), 1.   Google Scholar

[29]

S. E. Luczak, I. G. Rosen and J. Weiss, Determining blood and/or breath alcohol concentration from transdermal alcohol data, Proceedings of the 2013 American control conference,, International Federation of Automatic Control, (2013), 473.   Google Scholar

[30]

P. R. Marques and A. S. McKnight, Field and laboratory alcohol detection with 2 types of transdermal devices,, Alcohol Clin Exp Res, 33 (2009), 703.   Google Scholar

[31]

D. B. Matthews and W. R. Miller, Estimating blood alcohol concentration: Two computer programs and their applications in therapy and research,, Addictive Behaviors, 4 (1979), 55.   Google Scholar

[32]

I. Najfeld and T. F. Havel, Derivatives of the matrix exponential,, Advances in Applied Mathematics, 16 (1995), 321.  doi: 10.1006/aama.1995.1017.  Google Scholar

[33]

National Highway Traffic Safety Administration, Computing a BAC Estimate,, Department of Transportation, (1994).   Google Scholar

[34]

A. Okubo, Diffusion and Ecological Problems: Mathematical Models,, Springer-Verlag, (1980).   Google Scholar

[35]

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer-Verlag, (1983).  doi: 10.1007/978-1-4612-5561-1.  Google Scholar

[36]

A. J. Pritchard and D. Salamon, The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators,, SIAM J. Control and Optimization, 25 (1987), 121.  doi: 10.1137/0325009.  Google Scholar

[37]

I. G. Rosen, S. E. Luczak and J. Weiss, Blind deconvolution for distributed parameter systems with unbounded input and output and determining blood alcohol concentration from transdermal biosensor data,, Applied Math and Computation, 231 (2014), 357.  doi: 10.1016/j.amc.2013.12.099.  Google Scholar

[38]

I. G. Rosen, S. E. Luczak, W. Hu and M. Hankin, Discrete-time blind deconvolution for distributed parameter systems with Dirichlet boundary input and unbounded output with application to a transdermal alcohol biosensor,, Proceedings of 2013 SIAM Conference on Control and its Applications, (2013).   Google Scholar

[39]

J. T. Sakai, S. K. Mikulich-Gilbertson, R. J. Long and T. J. Crowley, Validity of transdermal alcohol monitoring: Fixed and self-regulated dosing,, Alcohol Clin Exp Res, 30 (2006), 26.   Google Scholar

[40]

M. Schultz, Spline Analysis,, Prentice Hall, (1973).   Google Scholar

[41]

R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,, London, (1977).   Google Scholar

[42]

L. C. Sobell and M. C. Sobell, Alcohol time-Line follow-back: A technique for assessing self-reported alcohol consumption, In R. Z. Litten and J. P. Allens (Eds.), Measuring Alcohol Consumption,, Humana Press, (1992).   Google Scholar

[43]

O. J. Staffans, Well-Posed Linear Systems,, Cambridge University Press, (2005).  doi: 10.1017/CBO9780511543197.  Google Scholar

[44]

R. M. Swift, Direct measurement of alcohol and its metabolites,, Addiction, 98S (2003), 78.   Google Scholar

[45]

R. M. Swift and L. L. Swette, Assessment of ethanol consumption with a wearable, electronic ethanol sensor/recorder, In R. Litten, and J. Allen (Eds.), Measuring Alcohol Consumption: Psychosocial and biological methods,, Humana Press, (1992).   Google Scholar

[46]

H. Tanabe, Equations of Evolution,, Pitman, (1979).   Google Scholar

[47]

M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups,, Birkhauser, (2009).  doi: 10.1007/978-3-7643-8994-9.  Google Scholar

[48]

J. G. Wagner and J. A. Patel, Variations in absorption and elimination rates of ethyl alcohol in a single subject,, Research Communications in Chemical Pathology and Pharmacology, 4 (1972), 61.   Google Scholar

[49]

P. E. Watson, I. D. Watson and R. D. Batt, Total body water volumes for adult males and females estimated from simple anthropometric measurements,, American Journal of Clinical Nutrition, 33 (1980), 27.   Google Scholar

[50]

P. E. Watson, I. D. Watson and R. D. Batt, Prediction of blood alcohol concentrations in human subjects: Updating the Widmark equation,, Journal of Studies on Alcohol, 42 (1981), 547.   Google Scholar

[51]

G. D. Webster and H. C. Gabler, Feasibility of transdermal ethanol sensing for the detection of intoxicated drivers,, Annu Proc Assoc Adv Automot Med, 51 (2007), 449.   Google Scholar

[52]

G. D. Webster and H. C. Gabler, Modeling of transdermal transport of alcohol: effect of body mass and gender,, Biomedical Sciences Instrumentation, 44 (2007), 361.   Google Scholar

[53]

J. Wloka, Partial Differential Equations,, Cambridge University Press, (1987).  doi: 10.1017/CBO9781139171755.  Google Scholar

[1]

Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65

[2]

Huijuan Song, Bei Hu, Zejia Wang. Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 667-691. doi: 10.3934/dcdsb.2020084

[3]

Xiaofeng Ren, David Shoup. The impact of the domain boundary on an inhibitory system: Interior discs and boundary half discs. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3957-3979. doi: 10.3934/dcds.2020048

[4]

Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399

[5]

Franck Davhys Reval Langa, Morgan Pierre. A doubly splitting scheme for the Caginalp system with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 653-676. doi: 10.3934/dcdss.2020353

[6]

Mikhail I. Belishev, Sergey A. Simonov. A canonical model of the one-dimensional dynamical Dirac system with boundary control. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021003

[7]

Fang Li, Bo You. On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021024

[8]

Xianbo Sun, Zhanbo Chen, Pei Yu. Parameter identification on Abelian integrals to achieve Chebyshev property. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020375

[9]

Xin Guo, Lexin Li, Qiang Wu. Modeling interactive components by coordinate kernel polynomial models. Mathematical Foundations of Computing, 2020, 3 (4) : 263-277. doi: 10.3934/mfc.2020010

[10]

Max E. Gilmore, Chris Guiver, Hartmut Logemann. Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021001

[11]

Jiaquan Liu, Xiangqing Liu, Zhi-Qiang Wang. Sign-changing solutions for a parameter-dependent quasilinear equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020454

[12]

Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial & Management Optimization, 2021, 17 (1) : 317-337. doi: 10.3934/jimo.2019113

[13]

Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020055

[14]

Feifei Cheng, Ji Li. Geometric singular perturbation analysis of Degasperis-Procesi equation with distributed delay. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 967-985. doi: 10.3934/dcds.2020305

[15]

Chun Liu, Huan Sun. On energetic variational approaches in modeling the nematic liquid crystal flows. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 455-475. doi: 10.3934/dcds.2009.23.455

[16]

Yicheng Liu, Yipeng Chen, Jun Wu, Xiao Wang. Periodic consensus in network systems with general distributed processing delays. Networks & Heterogeneous Media, 2020  doi: 10.3934/nhm.2021002

[17]

Baoli Yin, Yang Liu, Hong Li, Zhimin Zhang. Approximation methods for the distributed order calculus using the convolution quadrature. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1447-1468. doi: 10.3934/dcdsb.2020168

[18]

Jean-Paul Chehab. Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021002

[19]

Liang Huang, Jiao Chen. The boundedness of multi-linear and multi-parameter pseudo-differential operators. Communications on Pure & Applied Analysis, 2021, 20 (2) : 801-815. doi: 10.3934/cpaa.2020291

[20]

Jun Zhou. Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5581-5590. doi: 10.3934/cpaa.2020252

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (38)
  • HTML views (0)
  • Cited by (11)

[Back to Top]