메뉴 건너뛰기




Volumn 70, Issue 7, 2010, Pages 2281-2307

An extension of the boundary integral method applied to periodic disinfection of a dynamic biofilm

Author keywords

Biofilm; Boundary integral; Disinfection; Mathematical model; Persister; Tolerance

Indexed keywords

ANTI-MICROBIAL AGENT; BACTERIAL BIOFILM; BATCH CULTURE; BOUNDARY INTEGRAL METHODS; BOUNDARY INTEGRALS; EXPERIMENTAL OBSERVATION; FLUID FLOW; HETEROGENEOUS DISTRIBUTIONS; PERSISTER; PERSISTER CELLS; POLYMERIC SUBSTANCE; SPATIAL DOMAINS; TIME-SCALES; TOLERANCE; TOLERANCE MECHANISMS; TWO DIMENSIONAL MODEL;

EID: 77956236423     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090745532     Document Type: Article
Times cited : (12)

References (70)
  • 1
    • 34249703402 scopus 로고    scopus 로고
    • Description of mechanical response including detachment using a novel particle method of biofilm/flow interaction
    • E. Alpkvist and I. Klapper, Description of mechanical response including detachment using a novel particle method of biofilm/flow interaction, Water Sci. Tech., 55 (2007), pp. 265-273.
    • (2007) Water Sci. Tech. , vol.55 , pp. 265-273
    • Alpkvist, E.1    Klapper, I.2
  • 2
    • 0033930831 scopus 로고    scopus 로고
    • Role of antibiotic penetration limitation in Klebsiella pneumoniae biofilm resistance to ampicillin and ciprofloxacin
    • J. N. Anderl, M. J. Franklin, and P. S. Stewart, Role of antibiotic penetration limitation in Klebsiella pneumoniae biofilm resistance to ampicillin and ciprofloxacin, Antimicrobial Agents and Chemotherapy, 44 (2000), pp. 1818-1824.
    • (2000) Antimicrobial Agents and Chemotherapy , vol.44 , pp. 1818-1824
    • Anderl, J.N.1    Franklin, M.J.2    Stewart, P.S.3
  • 3
    • 27744488803 scopus 로고    scopus 로고
    • Modelling antibiotic-and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population
    • K. Anguige, J. King, and J. Ward, Modelling antibiotic-and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population, J. Math. Biol., 51 (2005), pp. 557-594.
    • (2005) J. Math. Biol. , vol.51 , pp. 557-594
    • Anguige, K.1    King, J.2    Ward, J.3
  • 4
    • 7444244983 scopus 로고    scopus 로고
    • Mathematical modelling of therapies targeted at bacterial quorum sensing
    • K. Anguige, J. King, J. Ward, and P. Williams, Mathematical modelling of therapies targeted at bacterial quorum sensing, Math. Biosci., 192 (2004), pp. 39-83.
    • (2004) Math. Biosci. , vol.192 , pp. 39-83
    • Anguige, K.1    King, J.2    Ward, J.3    Williams, P.4
  • 5
    • 36448959556 scopus 로고    scopus 로고
    • A multiscale model of biofilm as a senescence-structured fluid
    • B. P. Ayati and I. Klapper, A multiscale model of biofilm as a senescence-structured fluid, Multiscale Model. Simul., 6 (2007), pp. 347-365.
    • (2007) Multiscale Model. Simul. , vol.6 , pp. 347-365
    • Ayati, B.P.1    Klapper, I.2
  • 9
    • 0042410892 scopus 로고    scopus 로고
    • A method for computing nearly singular integrals
    • J. T. Beale and M.-C. Lai, A method for computing nearly singular integrals, SIAMJ.Numer. Anal., 38 (2001), pp. 1902-1925.
    • (2001) SIAMJ.Numer. Anal. , vol.38 , pp. 1902-1925
    • Beale, J.T.1    Lai, M.-C.2
  • 10
    • 33644941188 scopus 로고    scopus 로고
    • A three-dimensional computer model of four hypothetical mechanisms protecting biofilms from antimicrobials
    • J. D. Chambless, S. M. Hunt, and P. S. Stewart, A three-dimensional computer model of four hypothetical mechanisms protecting biofilms from antimicrobials, Appl. Environ. Microbiol., 72 (2006), pp. 2005-2013.
    • (2006) Appl. Environ. Microbiol. , vol.72 , pp. 2005-2013
    • Chambless, J.D.1    Hunt, S.M.2    Stewart, P.S.3
  • 11
    • 0004227066 scopus 로고
    • John Wiley & Sons, New York
    • W. Characklis, Biofilms, John Wiley & Sons, New York, 1990.
    • (1990) Biofilms
    • Characklis, W.1
  • 12
    • 0036381958 scopus 로고    scopus 로고
    • Role of electrostatic interactions in cohesion of bacterial biofilms
    • X. Chen and P. Stewart, Role of electrostatic interactions in cohesion of bacterial biofilms, Appl. Microbiol. Biotechnol., 59 (2002), pp. 718-720.
    • (2002) Appl. Microbiol. Biotechnol. , vol.59 , pp. 718-720
    • Chen, X.1    Stewart, P.2
  • 13
    • 3042785070 scopus 로고    scopus 로고
    • The role of the biofilm matrix in structural development
    • N. G. Cogan, The role of the biofilm matrix in structural development, Math. Medicine Biol., 21 (2004), pp. 147-166.
    • (2004) Math. Medicine Biol. , vol.21 , pp. 147-166
    • Cogan, N.G.1
  • 14
    • 30444453829 scopus 로고    scopus 로고
    • Effects of persister formation on bacterial response to dosing
    • N. G. Cogan, Effects of persister formation on bacterial response to dosing, J. Theoret. Biol., 238 (2006), pp. 694-703.
    • (2006) J. Theoret. Biol. , vol.238 , pp. 694-703
    • Cogan, N.G.1
  • 15
    • 41049089005 scopus 로고    scopus 로고
    • Hybrid numerical treatment of two fluid problems with passive interfaces
    • N. G. Cogan, Hybrid numerical treatment of two fluid problems with passive interfaces, Comm. Appl. Math. Comput. Sci., 2 (2007), pp. 117-133.
    • (2007) Comm. Appl. Math. Comput. Sci. , vol.2 , pp. 117-133
    • Cogan, N.G.1
  • 16
    • 34548015005 scopus 로고    scopus 로고
    • Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics
    • N. G. Cogan, Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics, J. Theoret. Biol., 248 (2007), pp. 340-349.
    • (2007) J. Theoret. Biol. , vol.248 , pp. 340-349
    • Cogan, N.G.1
  • 17
    • 41049097328 scopus 로고    scopus 로고
    • A two-fluid model of biofilm disinfection
    • N. G. Cogan, A two-fluid model of biofilm disinfection, Bull. Math. Biol., 70 (2008), pp. 800-819.
    • (2008) Bull. Math. Biol. , vol.70 , pp. 800-819
    • Cogan, N.G.1
  • 18
    • 19044385003 scopus 로고    scopus 로고
    • Modeling physiological resistance in bacterial biofilms
    • N. G. Cogan, R. Cortez, and L. J. Fauci, Modeling physiological resistance in bacterial biofilms, Bull. Math. Biol., 67 (2005), pp. 831-853.
    • (2005) Bull. Math. Biol. , vol.67 , pp. 831-853
    • Cogan, N.G.1    Cortez, R.2    Fauci, L.J.3
  • 19
    • 3042785070 scopus 로고    scopus 로고
    • The role of the biofilm matrix in structural development
    • N. G. Cogan and J. P. Keener, The role of the biofilm matrix in structural development, Math. Med. Biol., 21 (2004), pp. 147-166.
    • (2004) Math. Med. Biol. , vol.21 , pp. 147-166
    • Cogan, N.G.1    Keener, J.P.2
  • 20
    • 0036347671 scopus 로고    scopus 로고
    • The method of regularized Stokeslets
    • R. Cortez, The method of regularized Stokeslets, SIAM J. Sci. Comput., 23 (2001), pp. 1204-1225.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 1204-1225
    • Cortez, R.1
  • 21
    • 15844383109 scopus 로고    scopus 로고
    • The method of regularized Stokeslets in three dimensions: Analysis, validation, and application to helical swimming
    • R. Cortez, L. Fauci, and A. Medovikov, The method of regularized Stokeslets in three dimensions: Analysis, validation, and application to helical swimming, Phys. Fluids., 17 (2005), pp. 1-14.
    • (2005) Phys. Fluids. , vol.17 , pp. 1-14
    • Cortez, R.1    Fauci, L.2    Medovikov, A.3
  • 22
    • 0035252930 scopus 로고    scopus 로고
    • Cystic fibrosis pathogenesis and the role of biofilms in persistent infection
    • J. Costerton, Cystic fibrosis pathogenesis and the role of biofilms in persistent infection, Trends Microbiol., 9 (2001), pp. 50-52.
    • (2001) Trends Microbiol. , vol.9 , pp. 50-52
    • Costerton, J.1
  • 23
    • 0033591467 scopus 로고    scopus 로고
    • Bacterial biofilms: A common cause of persistent infections
    • J. Costerton, P. Stewart, and E. Greenberg, Bacterial biofilms: A common cause of persistent infections, Science, 284 (1999), pp. 1318-1322.
    • (1999) Science , vol.284 , pp. 1318-1322
    • Costerton, J.1    Stewart, P.2    Greenberg, E.3
  • 26
    • 33846150955 scopus 로고    scopus 로고
    • A mathematical formulation of the boundary integral equations for a compressible Stokes flow
    • F. R. Cunha, A. J. de Sousai, and M. Loewenberg, A mathematical formulation of the boundary integral equations for a compressible Stokes flow, Math. Appl. Comput., 22 (2003), pp. 53-73.
    • (2003) Math. Appl. Comput. , vol.22 , pp. 53-73
    • Cunha, F.R.1    De Sousai, A.J.2    Loewenberg, M.3
  • 27
    • 0037313237 scopus 로고    scopus 로고
    • Understanding biofilm resistance to antibacterial agents
    • D. Davies, Understanding biofilm resistance to antibacterial agents, Nature Rev. Drug Discovery, 2 (2003), pp. 114-122.
    • (2003) Nature Rev. Drug Discovery , vol.2 , pp. 114-122
    • Davies, D.1
  • 28
    • 0031825434 scopus 로고    scopus 로고
    • Increasing resistance of planktonic and biofilm cultures of Burkholderia cepeciax to ciproflaxacin and ceftazidime during exponential growth
    • M. Desai, T. Buhler, P. Weller, and M. Brown, Increasing resistance of planktonic and biofilm cultures of Burkholderia cepeciax to ciproflaxacin and ceftazidime during exponential growth, J. Antimicrobial Chemotherapy, 42 (1998), pp. 153-160.
    • (1998) J. Antimicrobial Chemotherapy , vol.42 , pp. 153-160
    • Desai, M.1    Buhler, T.2    Weller, P.3    Brown, M.4
  • 29
    • 0036302101 scopus 로고    scopus 로고
    • Finger formation in biofilm layers
    • J. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM J. Appl. Math., 62 (2001), pp. 853-869.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 853-869
    • Dockery, J.1    Klapper, I.2
  • 30
  • 31
    • 47849108516 scopus 로고    scopus 로고
    • Exposure of biofilms to slow flow fields: The convective contribution to growth and disinfection
    • H. J. Eberl and R. Sudarsan, Exposure of biofilms to slow flow fields: The convective contribution to growth and disinfection, J. Theoret. Biol., 253 (2008), pp. 788-807.
    • (2008) J. Theoret. Biol. , vol.253 , pp. 788-807
    • Eberl, H.J.1    Sudarsan, R.2
  • 33
    • 0000968412 scopus 로고    scopus 로고
    • Boundary integral methods for multicomponent fluids and multiphase fluids
    • T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, Boundary integral methods for multicomponent fluids and multiphase fluids, J. Comput. Phys., 169 (2001), pp. 302-362.
    • (2001) J. Comput. Phys. , vol.169 , pp. 302-362
    • Hou, T.Y.1    Lowengrub, J.S.2    Shelley, M.J.3
  • 34
    • 34547489403 scopus 로고    scopus 로고
    • The pharmacodynamics of antibiotic treatment
    • M. Imran and H. L. Smith, The pharmacodynamics of antibiotic treatment, J. Comput. Math. Methods Med., 7 (2006), pp. 229-263.
    • (2006) J. Comput. Math. Methods Med. , vol.7 , pp. 229-263
    • Imran, M.1    Smith, H.L.2
  • 36
    • 10044266575 scopus 로고    scopus 로고
    • Specialized persister cells and the mechanism of multidrug tolerance in Escherichia coli
    • I. Keren, D. Shah, A. Spoering, N. Kaldalu, and K. Lewis, Specialized persister cells and the mechanism of multidrug tolerance in Escherichia coli, J. Bacteriol., 186 (2004), pp. 8172-8180.
    • (2004) J. Bacteriol. , vol.186 , pp. 8172-8180
    • Keren, I.1    Shah, D.2    Spoering, A.3    Kaldalu, N.4    Lewis, K.5
  • 38
    • 0037027377 scopus 로고    scopus 로고
    • Viscoelastic fluid description of bacterial biofilm material properties
    • I. Klapper, C. Rupp, R. Cargo, B. Purvedorj, and P. Stoodley, Viscoelastic fluid description of bacterial biofilm material properties, Biotechnol. Bioeng., 80 (2002), pp. 289-296.
    • (2002) Biotechnol. Bioeng. , vol.80 , pp. 289-296
    • Klapper, I.1    Rupp, C.2    Cargo, R.3    Purvedorj, B.4    Stoodley, P.5
  • 39
    • 0035002909 scopus 로고    scopus 로고
    • Modelling production of extracellular polymeric substances in a Pseudomonas aeruginosa chemostat culture
    • J. D. R. Kommedal, R. Bakke, and P. Stoodley, Modelling production of extracellular polymeric substances in a Pseudomonas aeruginosa chemostat culture, Water Sci. Technol., 43 (2001), pp. 129-134.
    • (2001) Water Sci. Technol. , vol.43 , pp. 129-134
    • Kommedal, J.D.R.1    Bakke, R.2    Stoodley, P.3
  • 41
    • 41849094833 scopus 로고    scopus 로고
    • An efficient numerical method for the two-fluid Stokes equations with a moving boundary
    • A. T. Layton, An efficient numerical method for the two-fluid Stokes equations with a moving boundary, Comput. Methods Appl. Mech. Engrg., 197 (2007), pp. 2147-2155.
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 2147-2155
    • Layton, A.T.1
  • 42
    • 70349908259 scopus 로고    scopus 로고
    • Failure of antibiotic treatment in microbial populations
    • P. De Leenheer and N. G. Cogan, Failure of antibiotic treatment in microbial populations, J. Math. Biol., 59 (2009), pp. 563-579.
    • (2009) J. Math. Biol. , vol.59 , pp. 563-579
    • De Leenheer, P.1    Cogan, N.G.2
  • 44
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • R. J. Leveque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31 (1994), pp. 1019-1044.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1019-1044
    • Leveque, R.J.1    Li, Z.2
  • 45
    • 33745189789 scopus 로고    scopus 로고
    • Noninherited antibiotic resistance
    • B. R. Levin and D. E. Rozen, Noninherited antibiotic resistance, Nature Rev. Microbiol., 4 (2006), pp. 556-562.
    • (2006) Nature Rev. Microbiol. , vol.4 , pp. 556-562
    • Levin, B.R.1    Rozen, D.E.2
  • 48
    • 0032485575 scopus 로고    scopus 로고
    • Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach
    • C. Picioreanu, M. C. M. van Loosdrecht, and J. J. Heijnen, Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach, Biotechnol. Bioeng., 58 (2000), pp. 101-116.
    • (2000) Biotechnol. Bioeng. , vol.58 , pp. 101-116
    • Picioreanu, C.1    Van Loosdrecht, M.C.M.2    Heijnen, J.J.3
  • 49
    • 0027264175 scopus 로고
    • Use of rRNA fluorescence in situ hybridization for measuring the activity of single cells in young and established biofilms
    • L. K. Poulsen, G. Ballard, and D. A. Stahl, Use of rRNA fluorescence in situ hybridization for measuring the activity of single cells in young and established biofilms, Appl. Environ. Microbiol., 59 (1993), pp. 1354-1360.
    • (1993) Appl. Environ. Microbiol. , vol.59 , pp. 1354-1360
    • Poulsen, L.K.1    Ballard, G.2    Stahl, D.A.3
  • 51
    • 0035840109 scopus 로고    scopus 로고
    • Expansion of a compressible gas bubble in Stokes flow
    • C. Pozrikidis, Expansion of a compressible gas bubble in Stokes flow, J. Fluid Mech., 442 (2001), pp. 171-189.
    • (2001) J. Fluid Mech. , vol.442 , pp. 171-189
    • Pozrikidis, C.1
  • 52
    • 0000736524 scopus 로고    scopus 로고
    • Interfacial dynamics for Stokes flow
    • C. Pozrikidis, Interfacial dynamics for Stokes flow, J. Comput. Phys., 169 (2001), pp. 250-301.
    • (2001) J. Comput. Phys. , vol.169 , pp. 250-301
    • Pozrikidis, C.1
  • 54
    • 0346732025 scopus 로고    scopus 로고
    • Modeling antibiotic tolerance in biofilms by accounting for nutrient limitation
    • M. E. Roberts and P. S. Stewart, Modeling antibiotic tolerance in biofilms by accounting for nutrient limitation, Antimicrobial Agents and Chemotherapy, 48 (2004), pp. 48-52.
    • (2004) Antimicrobial Agents and Chemotherapy , vol.48 , pp. 48-52
    • Roberts, M.E.1    Stewart, P.S.2
  • 55
    • 0021675168 scopus 로고
    • Cellular reproduction and extracellular polymer formation by Pseudomonas aeruginosa in continuous culture
    • J. A. Robinson, M. G. Trulear, and W. G. Characklis, Cellular reproduction and extracellular polymer formation by Pseudomonas aeruginosa in continuous culture, Biotechnol. Bioeng., 26 (1984), pp. 1409-1417.
    • (1984) Biotechnol. Bioeng. , vol.26 , pp. 1409-1417
    • Robinson, J.A.1    Trulear, M.G.2    Characklis, W.G.3
  • 56
    • 1842370842 scopus 로고    scopus 로고
    • Evidence of bacterial adaption to monochloramine in Pseudomonas aeruginosa biofilms and evaluation of biocide action model
    • S. S. Sanderson and P. S. Stewart, Evidence of bacterial adaption to monochloramine in Pseudomonas aeruginosa biofilms and evaluation of biocide action model, Biotechnol. Bioeng., 56 (1997), pp. 201-209.
    • (1997) Biotechnol. Bioeng. , vol.56 , pp. 201-209
    • Sanderson, S.S.1    Stewart, P.S.2
  • 58
    • 0035723050 scopus 로고    scopus 로고
    • Biofilm penetration and disinfection efficacy of alkaline hypochlorite and chlorosulfamates
    • P. Stewart, J. Rayner, F. Roe, and W. Rees, Biofilm penetration and disinfection efficacy of alkaline hypochlorite and chlorosulfamates, J. Appl. Microbiol., 91 (2001), pp. 525-532.
    • (2001) J. Appl. Microbiol. , vol.91 , pp. 525-532
    • Stewart, P.1    Rayner, J.2    Roe, F.3    Rees, W.4
  • 59
    • 0029981119 scopus 로고    scopus 로고
    • Theoretical aspects of antibiotic diffusion into microbial biofilms
    • P. S. Stewart, Theoretical aspects of antibiotic diffusion into microbial biofilms, Antimicrobial Agents and Chemotherapy, 40 (1996), pp. 2517-2522.
    • (1996) Antimicrobial Agents and Chemotherapy , vol.40 , pp. 2517-2522
    • Stewart, P.S.1
  • 60
    • 77956250076 scopus 로고    scopus 로고
    • Biofilm material properties as related to shear-induced deformation and detachment phenomena
    • P. Stoodley, R. Cargo, C. J. Rupp, S. Wilson, and I. Klapper, Biofilm material properties as related to shear-induced deformation and detachment phenomena, J. Industrial Microbiol. Biotech., 361 (2002), pp. 1476-5535.
    • (2002) J. Industrial Microbiol. Biotech. , vol.361 , pp. 1476-5535
    • Stoodley, P.1    Cargo, R.2    Rupp, C.J.3    Wilson, S.4    Klapper, I.5
  • 61
    • 0344736962 scopus 로고    scopus 로고
    • Clonal variation in maximum specific growth rate and susceptibility towards antimicrobials
    • N. Sufya, D. Allison, and P. Gilbert, Clonal variation in maximum specific growth rate and susceptibility towards antimicrobials, J. Appl. Microbiol., 95 (2003), pp. 1261-1267.
    • (2003) J. Appl. Microbiol. , vol.95 , pp. 1261-1267
    • Sufya, N.1    Allison, D.2    Gilbert, P.3
  • 64
    • 0022678081 scopus 로고
    • A multispecies biofilm model
    • O. Wanner and W. Gujer, A multispecies biofilm model, Biotechnol. Bioeng., 28 (1986), pp. 314-328.
    • (1986) Biotechnol. Bioeng. , vol.28 , pp. 314-328
    • Wanner, O.1    Gujer, W.2
  • 65
    • 4344702253 scopus 로고    scopus 로고
    • Biofilm modeling with AQUASIM
    • O. Wanner and E. Morgenroth, Biofilm modeling with AQUASIM, Water Sci. Technol., 49 (2004), pp. 137-144.
    • (2004) Water Sci. Technol. , vol.49 , pp. 137-144
    • Wanner, O.1    Morgenroth, E.2
  • 66
    • 0034015354 scopus 로고    scopus 로고
    • Biofilm, City of microbes
    • P. Watnick and R. Kolter, Biofilm, City of microbes, J. Bacteriol., 182 (2000), pp. 2675-2679.
    • (2000) J. Bacteriol. , vol.182 , pp. 2675-2679
    • Watnick, P.1    Kolter, R.2
  • 67
    • 0031031474 scopus 로고    scopus 로고
    • A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models
    • J. W. Wimpenny and R. Colasanti, A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models, FEMS Microbiol. Ecol., 22 (2006), pp. 1-16.
    • (2006) FEMS Microbiol. Ecol. , vol.22 , pp. 1-16
    • Wimpenny, J.W.1    Colasanti, R.2
  • 68
    • 0034057759 scopus 로고    scopus 로고
    • Biofilm resistance to antimicrobial agents
    • K. D. Xu, G. A. McFeters, and P. S. Stewart, Biofilm resistance to antimicrobial agents, Microbiology, 146 (2000), pp. 547-549.
    • (2000) Microbiology , vol.146 , pp. 547-549
    • Xu, K.D.1    McFeters, G.A.2    Stewart, P.S.3
  • 69
    • 50049125083 scopus 로고    scopus 로고
    • Field-phase models for biofilms. II. 2-d numerical simulations of biofilm-flow interaction
    • T. Zhang, N. G. Cogan, and Q. Wang, Field-phase models for biofilms. II. 2-d numerical simulations of biofilm-flow interaction, Comm. Comput. Phys., 4 (2008), pp. 72-101.
    • (2008) Comm. Comput. Phys. , vol.4 , pp. 72-101
    • Zhang, T.1    Cogan, N.G.2    Wang, Q.3
  • 70
    • 57349099645 scopus 로고    scopus 로고
    • Phase field models for biofilms. I. Theory and onedimensional simulations
    • T. Zhang, N. G. Cogan, and Q. Wang, Phase field models for biofilms. I. Theory and onedimensional simulations, SIAM J. Appl. Math., 69 (2008), pp. 641-669.
    • (2008) SIAM J. Appl. Math. , vol.69 , pp. 641-669
    • Zhang, T.1    Cogan, N.G.2    Wang, Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.