메뉴 건너뛰기




Volumn 93, Issue 4, 2003, Pages 655-673

Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0242389718     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110200406     Document Type: Article
Times cited : (101)

References (32)
  • 1
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • H. Alt and S. Luckhaus. Quasilinear elliptic-parabolic differential equations. Math. Z. 183: 311-341 (1983)
    • (1983) Math. Z. , vol.183 , pp. 311-341
    • Alt, H.1    Luckhaus, S.2
  • 2
    • 0002158619 scopus 로고
    • Reaction-diffusion problems in electrolysis
    • H. Amann and M. Renardy. Reaction-diffusion problems in electrolysis. Nonlin. Diff. Eqs. Appl. 1: 91-117 (1994)
    • (1994) Nonlin. Diff. Eqs. Appl. , vol.1 , pp. 91-117
    • Amann, H.1    Renardy, M.2
  • 3
    • 21844491367 scopus 로고
    • Multi-dimensional electrochemistry model
    • Y. Choi and R. Lui. Multi-dimensional electrochemistry model. Arch. Rat. Mech. Anal. 130: 315-342 (1995)
    • (1995) Arch. Rat. Mech. Anal. , vol.130 , pp. 315-342
    • Choi, Y.1    Lui, R.2
  • 4
    • 0031280714 scopus 로고    scopus 로고
    • Symmetrization and entropy inequality for general diffusion equations
    • P. Degond, S. Génieys, and A. Jüngel. Symmetrization and entropy inequality for general diffusion equations. C. R. Acad. Sci. Paris 325: 963-968 (1997)
    • (1997) C. R. Acad. Sci. Paris , vol.325 , pp. 963-968
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 5
    • 0031521314 scopus 로고    scopus 로고
    • A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects
    • P. Degond, S. Génieys, and A. Jüngel. A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects. J. Math. Pures Appl. 76: 991-1015 (1997)
    • (1997) J. Math. Pures Appl. , vol.76 , pp. 991-1015
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 6
    • 0000329021 scopus 로고
    • An initial-boundary value problem for a certain density-dependent diffusion system
    • P. Deuring. An initial-boundary value problem for a certain density-dependent diffusion system. Math. Z. 194: 375-396 (1987)
    • (1987) Math. Z. , vol.194 , pp. 375-396
    • Deuring, P.1
  • 9
    • 0032445844 scopus 로고    scopus 로고
    • Global behaviour of a reaction-diffusion system modelling chemotaxis
    • H. Gajewski and K. Zacharias. Global behaviour of a reaction-diffusion system modelling chemotaxis. Math. Nachr. 195: 77-114 (1998)
    • (1998) Math. Nachr. , vol.195 , pp. 77-114
    • Gajewski, H.1    Zacharias, K.2
  • 10
    • 4544271264 scopus 로고    scopus 로고
    • Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics
    • G. Galiano, M. Garzón, and A. Jüngel. Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics. To appear in Rev. Real Acad. Ciencias Serie A. Mat., 2002
    • (2002) Rev. Real Acad. Ciencias Serie A. Mat.
    • Galiano, G.1    Garzón, M.2    Jüngel, A.3
  • 11
    • 0002917438 scopus 로고    scopus 로고
    • A quantum regularization of the one-dimensional hydrodynamic model for semiconductors
    • M. T. Gyi and A. Jüngel. A quantum regularization of the one-dimensional hydrodynamic model for semiconductors. Adv. Diff. Eqs. 5: 773-800 (2000)
    • (2000) Adv. Diff. Eqs. , vol.5 , pp. 773-800
    • Gyi, M.T.1    Jüngel, A.2
  • 14
    • 0002387420 scopus 로고    scopus 로고
    • A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations
    • A. Jüngel and Y.-J. Peng. A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations. Annales H. Poincaré 17: 83-118 (2000)
    • (2000) Annales H. Poincaré , vol.17 , pp. 83-118
    • Jüngel, A.1    Peng, Y.-J.2
  • 15
    • 0034353705 scopus 로고    scopus 로고
    • Global non-negative solutions of a fourth-order nonlinear parabolic equation for quantum systems
    • A. Jüngel and R. Pinnau. Global non-negative solutions of a fourth-order nonlinear parabolic equation for quantum systems. To appear in SIAM J. Math. Anal., 2000
    • (2000) SIAM J. Math. Anal.
    • Jüngel, A.1    Pinnau, R.2
  • 16
    • 0035322533 scopus 로고    scopus 로고
    • A positivity-preserving numerical scheme for a fourth-order parabolic equation
    • A. Jüngel and R. Pinnau. A positivity-preserving numerical scheme for a fourth-order parabolic equation. SIAM J. Num. Anal. 39: 385-406 (2001)
    • (2001) SIAM J. Num. Anal. , vol.39 , pp. 385-406
    • Jüngel, A.1    Pinnau, R.2
  • 17
    • 84862599035 scopus 로고
    • Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
    • A. S. Kalashnikov. Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations. Russ. Math. Surveys 42: 169-222 (1987)
    • (1987) Russ. Math. Surveys , vol.42 , pp. 169-222
    • Kalashnikov, A.S.1
  • 18
    • 0000297309 scopus 로고
    • Smooth solutions to a quasi-linear system of diffusion equations for a certain population model
    • J.U. Kim. Smooth solutions to a quasi-linear system of diffusion equations for a certain population model. Nonlin. Anal. 8: 1121-1144 (1984)
    • (1984) Nonlin. Anal. , vol.8 , pp. 1121-1144
    • Kim, J.U.1
  • 19
    • 0030579038 scopus 로고    scopus 로고
    • Diffusion, self-diffusion and cross-diffusion
    • Y. Lou and W.-M. Ni. Diffusion, self-diffusion and cross-diffusion. J. Diff. Eqs. 131: 79-131 (1996)
    • (1996) J. Diff. Eqs. , vol.131 , pp. 79-131
    • Lou, Y.1    Ni, W.-M.2
  • 20
    • 0242608980 scopus 로고    scopus 로고
    • The global existence of solutions for a cross-diffusion system
    • Y. Lou, W.-M. Ni, and Y. Wu. The global existence of solutions for a cross-diffusion system. Adv. Math., Beijing 25: 283-284 (1996)
    • (1996) Adv. Math., Beijing , vol.25 , pp. 283-284
    • Lou, Y.1    Ni, W.-M.2    Wu, Y.3
  • 22
    • 0018830043 scopus 로고
    • Spatial segregation in competitive interaction-diffusion equations
    • M. Mimura and K. Kawasaki. Spatial segregation in competitive interaction-diffusion equations. J. Math. Biol. 9: 49-64 (1980)
    • (1980) J. Math. Biol. , vol.9 , pp. 49-64
    • Mimura, M.1    Kawasaki, K.2
  • 24
    • 0001637925 scopus 로고
    • Global existence of solutions for a strongly coupled quasilinear parabolic system
    • M. Pozio and A. Tesei. Global existence of solutions for a strongly coupled quasilinear parabolic system. Nonlin. Anal. 14: 657-689 (1990)
    • (1990) Nonlin. Anal. , vol.14 , pp. 657-689
    • Pozio, M.1    Tesei, A.2
  • 25
    • 0001294750 scopus 로고
    • Existence of the global attractor for a strongly coupled parabolic system arising in population dynamics
    • R. Redlinger. Existence of the global attractor for a strongly coupled parabolic system arising in population dynamics. J. Diff. Eqs. 118: 219-252 (1995)
    • (1995) J. Diff. Eqs. , vol.118 , pp. 219-252
    • Redlinger, R.1
  • 26
    • 0029690507 scopus 로고    scopus 로고
    • Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients
    • W. Ruan. Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients. J. Math. Anal. Appl. 197: 558-578 (1996)
    • (1996) J. Math. Anal. Appl. , vol.197 , pp. 558-578
    • Ruan, W.1
  • 30
    • 0038225135 scopus 로고    scopus 로고
    • Global solutions to some quasilinear parabolic systems in population dynamics
    • Y. Wanli. Global solutions to some quasilinear parabolic systems in population dynamics. J. Partial Diff. Eqs. 12: 193-200 (1999)
    • (1999) J. Partial Diff. Eqs. , vol.12 , pp. 193-200
    • Wanli, Y.1
  • 31
    • 0242693061 scopus 로고    scopus 로고
    • Qualitative studies of solutions for some cross-diffusion systems
    • T.-T. Li, M. Mimura, Y. Nishiura, and Q.-X. Ye, editors, World Scientific
    • Y. Wu. Qualitative studies of solutions for some cross-diffusion systems. In T.-T. Li, M. Mimura, Y. Nishiura, and Q.-X. Ye, editors, China-Japan Symposium on Reaction-Diffusion Eqautions and Their Applications and Computational Aspects, pages 177-187 (Singapore, 1997) World Scientific
    • (1997) China-Japan Symposium on Reaction-diffusion Eqautions and Their Applications and Computational Aspects , pp. 177-187
    • Wu, Y.1
  • 32
    • 38248999657 scopus 로고
    • Global solution to some quasilinear parabolic system in population dynamics
    • A. Yagi. Global solution to some quasilinear parabolic system in population dynamics. Nonlin. Anal. 21: 603-630 (1993)
    • (1993) Nonlin. Anal. , vol.21 , pp. 603-630
    • Yagi, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.