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Volumn 92, Issue 6, 2009, Pages 651-667

Conservative cross diffusions and pattern formation through relaxation

Author keywords

Cross diffusions; Duality method; Patch formation; Turing instability

Indexed keywords


EID: 72149113041     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2009.05.003     Document Type: Article
Times cited : (37)

References (34)
  • 1
    • 45549120045 scopus 로고
    • Dynamic theory of quasilinear parabolic equations. I. Abstract evolution equations
    • Amann H. Dynamic theory of quasilinear parabolic equations. I. Abstract evolution equations. Nonlinear Anal. 12 (1988) 895-919
    • (1988) Nonlinear Anal. , vol.12 , pp. 895-919
    • Amann, H.1
  • 2
    • 84972541997 scopus 로고
    • Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems
    • Amann H. Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems. Differential Integral Equations 3 (1990) 13-75
    • (1990) Differential Integral Equations , vol.3 , pp. 13-75
    • Amann, H.1
  • 3
    • 0001742516 scopus 로고
    • Erratum: "Dynamic theory of quasilinear parabolic systems. III. Global existence"
    • MR1013086 (90i:35125)
    • Amann H. Erratum: "Dynamic theory of quasilinear parabolic systems. III. Global existence". Math. Z. 202 2 (1989) 219-250 MR1013086 (90i:35125)
    • (1989) Math. Z. , vol.202 , Issue.2 , pp. 219-250
    • Amann, H.1
  • 4
    • 51249176588 scopus 로고
    • Erratum: "Dynamic theory of quasilinear parabolic systems. III. Global existence"
    • Amann H. Erratum: "Dynamic theory of quasilinear parabolic systems. III. Global existence". Math. Z. 205 (1990) 331
    • (1990) Math. Z. , vol.205 , pp. 331
    • Amann, H.1
  • 5
    • 58149280080 scopus 로고    scopus 로고
    • A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion
    • Anguige K., and Schmeiser C. A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion. J. Math. Biol. 58 3 (2009) 395-427
    • (2009) J. Math. Biol. , vol.58 , Issue.3 , pp. 395-427
    • Anguige, K.1    Schmeiser, C.2
  • 6
    • 0034288024 scopus 로고    scopus 로고
    • Global existence for coupled reaction-diffusion systems
    • Boudiba N., and Pierre M. Global existence for coupled reaction-diffusion systems. J. Math. Anal. Appl. 250 (2000) 1-12
    • (2000) J. Math. Anal. Appl. , vol.250 , pp. 1-12
    • Boudiba, N.1    Pierre, M.2
  • 7
    • 33645922467 scopus 로고    scopus 로고
    • Analysis of a parabolic cross-diffusion population model without self-diffusion
    • Chen L., and Jüngel A. Analysis of a parabolic cross-diffusion population model without self-diffusion. J. Differential Equations 224 (2006) 39-59
    • (2006) J. Differential Equations , vol.224 , pp. 39-59
    • Chen, L.1    Jüngel, A.2
  • 8
    • 33847127029 scopus 로고    scopus 로고
    • Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering
    • Chen L., and Jüngel A. Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering. Comm. Partial Differential Equations 32 (2007) 127-148
    • (2007) Comm. Partial Differential Equations , vol.32 , pp. 127-148
    • Chen, L.1    Jüngel, A.2
  • 9
    • 0031280714 scopus 로고    scopus 로고
    • Symmetrization and entropy inequality for general diffusion equations
    • Degond P., Génieys S., and Jüngel A. Symmetrization and entropy inequality for general diffusion equations. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 963-968
    • (1997) C. R. Acad. Sci. Paris Sér. I Math. , vol.325 , pp. 963-968
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 11
    • 13844271552 scopus 로고    scopus 로고
    • A survey of entropy methods for partial differential equations
    • (electronic)
    • Evans L.C. A survey of entropy methods for partial differential equations. Bull. Amer. Math. Soc. (N.S.) 41 (2004) 409-438 (electronic)
    • (2004) Bull. Amer. Math. Soc. (N.S.) , vol.41 , pp. 409-438
    • Evans, L.C.1
  • 12
    • 8744271402 scopus 로고    scopus 로고
    • Irreversibility and hysteresis for a forward-backward diffusion equation
    • Evans L.C., and Portilheiro M. Irreversibility and hysteresis for a forward-backward diffusion equation. Math. Models Methods Appl. Sci. 14 (2004) 1599-1620
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 1599-1620
    • Evans, L.C.1    Portilheiro, M.2
  • 13
    • 59849083764 scopus 로고    scopus 로고
    • An existence result to a strongly coupled degenerated system arising in tumor modeling
    • electronic, 19 pp
    • L. Hadjadj, K. Hamdache, D. Hamroun, An existence result to a strongly coupled degenerated system arising in tumor modeling, Abstr. Appl. Anal. (2008), ID 239870, 19 pp. (electronic)
    • (2008) Abstr. Appl. Anal , vol.ID 239870
    • Hadjadj, L.1    Hamdache, K.2    Hamroun, D.3
  • 14
    • 33748291529 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion and competitive interaction
    • Iida M., Mimura M., and Ninomiya H. Diffusion, cross-diffusion and competitive interaction. J. Math. Biol. 53 (2006) 617-641
    • (2006) J. Math. Biol. , vol.53 , pp. 617-641
    • Iida, M.1    Mimura, M.2    Ninomiya, H.3
  • 15
    • 72149098649 scopus 로고    scopus 로고
    • Reaction-diffusion system approximation to the cross-diffusion competition system
    • Izuhara H., and Mimura M. Reaction-diffusion system approximation to the cross-diffusion competition system. Hiroshima Math. J. 38 (2008) 315-347
    • (2008) Hiroshima Math. J. , vol.38 , pp. 315-347
    • Izuhara, H.1    Mimura, M.2
  • 16
    • 84972554928 scopus 로고
    • On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws
    • Kawashima S., and Shizuta Y. On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws. Tohoku Math. J. (2) 40 (1988) 449-464
    • (1988) Tohoku Math. J. (2) , vol.40 , pp. 449-464
    • Kawashima, S.1    Shizuta, Y.2
  • 17
    • 72149088548 scopus 로고    scopus 로고
    • t. Lepoutre, Partial differential equations arising in biology, PhD thesis, Univ. P. et M. Curie, in preparation
    • t. Lepoutre, Partial differential equations arising in biology, PhD thesis, Univ. P. et M. Curie, in preparation
  • 18
    • 36849153282 scopus 로고
    • Hypothesis for origin of planktonic patchiness
    • Levin S., and Segel L. Hypothesis for origin of planktonic patchiness. Nature 259 (1976) 659
    • (1976) Nature , vol.259 , pp. 659
    • Levin, S.1    Segel, L.2
  • 19
    • 0000793907 scopus 로고
    • A more functional response to predator-prey stability
    • Levin S.A. A more functional response to predator-prey stability. The American Naturalist 108 (1977) 207-228
    • (1977) The American Naturalist , vol.108 , pp. 207-228
    • Levin, S.A.1
  • 20
    • 15744396864 scopus 로고    scopus 로고
    • Global existence of solutions to a cross-diffusion system in higher dimensional domains
    • Li Y., and Zhao C. Global existence of solutions to a cross-diffusion system in higher dimensional domains. Discrete Contin. Dynam. Systems 12 (2005) 185-192
    • (2005) Discrete Contin. Dynam. Systems , vol.12 , pp. 185-192
    • Li, Y.1    Zhao, C.2
  • 22
    • 0030579038 scopus 로고    scopus 로고
    • Diffusion, self-diffusion and cross-diffusion
    • Lou Y., and Ni W.-M. Diffusion, self-diffusion and cross-diffusion. J. Differential Equations 131 (1996) 79-131
    • (1996) J. Differential Equations , vol.131 , pp. 79-131
    • Lou, Y.1    Ni, W.-M.2
  • 23
    • 0344629886 scopus 로고    scopus 로고
    • Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
    • Marrocco A. Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. M2AN Math. Model. Numer. Anal. 37 (2003) 617-630
    • (2003) M2AN Math. Model. Numer. Anal. , vol.37 , pp. 617-630
    • Marrocco, A.1
  • 24
    • 0018830043 scopus 로고
    • Spatial segregation in competitive interaction-diffusion equations
    • Mimura M., and Kawasaki K. Spatial segregation in competitive interaction-diffusion equations. J. Math. Biol. 9 (1980) 49-64
    • (1980) J. Math. Biol. , vol.9 , pp. 49-64
    • Mimura, M.1    Kawasaki, K.2
  • 25
    • 0018224543 scopus 로고
    • On a diffusive prey-predator model which exhibits patchiness
    • Mimura M., and Murray J.D. On a diffusive prey-predator model which exhibits patchiness. J. Theoret. Biol. 75 (1978) 249-262
    • (1978) J. Theoret. Biol. , vol.75 , pp. 249-262
    • Mimura, M.1    Murray, J.D.2
  • 26
    • 0020024057 scopus 로고
    • Pattern formation in interacting and diffusing systems in population biology
    • Mimura M., and Yamaguti M. Pattern formation in interacting and diffusing systems in population biology. Adv. Biophys. 15 (1982) 19-65
    • (1982) Adv. Biophys. , vol.15 , pp. 19-65
    • Mimura, M.1    Yamaguti, M.2
  • 27
    • 0039565256 scopus 로고
    • Stable patterns in a viscous diffusion equation
    • Novick-Cohen A., and Pego R.L. Stable patterns in a viscous diffusion equation. Trans. Amer. Math. Soc. 324 (1991) 331-351
    • (1991) Trans. Amer. Math. Soc. , vol.324 , pp. 331-351
    • Novick-Cohen, A.1    Pego, R.L.2
  • 28
    • 0003334526 scopus 로고
    • Diffusion and Ecological Problems: Mathematical Models
    • Springer-Verlag, Berlin (an extended version of the Japanese edition, Ecology and Diffusion, translated by G.N. Parker)
    • Okubo A. Diffusion and Ecological Problems: Mathematical Models. Biomathematics vol. 10 (1980), Springer-Verlag, Berlin (an extended version of the Japanese edition, Ecology and Diffusion, translated by G.N. Parker)
    • (1980) Biomathematics , vol.10
    • Okubo, A.1
  • 29
    • 0141461783 scopus 로고    scopus 로고
    • 1 for reaction-diffusion systems
    • (dedicated to Philippe Bénilan)
    • 1 for reaction-diffusion systems. J. Evol. Equation 3 (2003) 153-168 (dedicated to Philippe Bénilan)
    • (2003) J. Evol. Equation , vol.3 , pp. 153-168
    • Pierre, M.1
  • 30
    • 0033730117 scopus 로고    scopus 로고
    • Blowup in reaction-diffusion systems with dissipation of mass
    • (electronic)
    • Pierre M., and Schmitt D. Blowup in reaction-diffusion systems with dissipation of mass. SIAM Rev. 42 (2000) 93-106 (electronic)
    • (2000) SIAM Rev. , vol.42 , pp. 93-106
    • Pierre, M.1    Schmitt, D.2
  • 31
    • 0012945863 scopus 로고
    • Passage to the limit with respect to viscosity in an equation with a variable direction of parabolicity
    • 734
    • Plotnikov P.I. Passage to the limit with respect to viscosity in an equation with a variable direction of parabolicity. Differentsialnye Uravneniya 30 (1994) 665-674 734
    • (1994) Differentsialnye Uravneniya , vol.30 , pp. 665-674
    • Plotnikov, P.I.1
  • 33
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • Turing A.M. The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. B 237 (1952) 83-99
    • (1952) Phil. Trans. Roy. Soc. B , vol.237 , pp. 83-99
    • Turing, A.M.1
  • 34
    • 23044472308 scopus 로고    scopus 로고
    • The global existence of solutions for a cross-diffusion system
    • Wang Y. The global existence of solutions for a cross-diffusion system. Acta Math. Appl. Sin. Engl. Ser. 21 (2005) 519-528
    • (2005) Acta Math. Appl. Sin. Engl. Ser. , vol.21 , pp. 519-528
    • Wang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.