메뉴 건너뛰기




Volumn 70, Issue 3, 2005, Pages 386-399

On some cross-diffusion models in population dynamics and their connections to well-posed filters in signal enhancement processes

Author keywords

Cross diffusion systems; Filters for signal enhancement processes; Local existence; Models for aggregation; Population dynamics; Schauder's fixed point theorem

Indexed keywords

LYAPUNOV METHODS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 20444393063     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/hxh036     Document Type: Article
Times cited : (1)

References (19)
  • 2
    • 0002071824 scopus 로고
    • The role of diffusion in mathematical population biology: Skellam revisited
    • Lecture Notes in Biomathematics. Berlin: Springer
    • Aronson, D. G. (1985) The role of diffusion in mathematical population biology: Skellam revisited. Proc. Int. Conf. on Mathematics in Biology and Medicine, 1983 Lecture Notes in Biomathematics Vol. 57. Berlin: Springer, pp. 2-6.
    • (1985) Proc. Int. Conf. on Mathematics in Biology and Medicine 1983 , vol.57 , pp. 2-6
    • Aronson, D.G.1
  • 3
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • Catté, F., Lions, P. -L., Morel, J. -M. & Coll, T. (1992) Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal., 29, 182-193.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 182-193
    • Catté, F.1    Lions, P.-L.2    Morel, J.-M.3    Coll, T.4
  • 5
    • 20444398945 scopus 로고    scopus 로고
    • From lattice to continuum: Aggregation under local reinforcement
    • to appear
    • Horstmann, D., Painter, K. J. & Othmer, H. G. (2003) From lattice to continuum: aggregation under local reinforcement. Eur. J. Appl. Math., to appear.
    • (2003) Eur. J. Appl. Math.
    • Horstmann, D.1    Painter, K.J.2    Othmer, H.G.3
  • 6
    • 0032382150 scopus 로고    scopus 로고
    • Maximum principle and comparison theorems for anisotropic diffusion
    • Kawohl, B. & Kutev, N. (1998) Maximum principle and comparison theorems for anisotropic diffusion. Math. Ann., 311, 107-123.
    • (1998) Math. Ann. , vol.311 , pp. 107-123
    • Kawohl, B.1    Kutev, N.2
  • 7
    • 0031256990 scopus 로고    scopus 로고
    • The Perona - Malik paradox
    • Kichenassamy, S. (1997) The Perona - Malik paradox. SIAM J. Appl. Math., 57, 1328-1342.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1328-1342
    • Kichenassamy, S.1
  • 9
    • 0042868726 scopus 로고    scopus 로고
    • 3rd edn, Interdisciplinary Applied Mathematics Series. Heidelberg: Springer
    • Murray, J. D. (2002) Mathematical Biology I: An Introduction 3rd edn, Interdisciplinary Applied Mathematics Series Vol. 17. Heidelberg: Springer.
    • (2002) Mathematical Biology I: An Introduction , vol.17
    • Murray, J.D.1
  • 10
    • 0039565256 scopus 로고
    • Stable patterns in a viscous diffusion equation
    • Novick-Cohen, A. & Pego, R. L. (1991) Stable patterns in a viscous diffusion equation. Trans. Am. Math. Soc., 324, 331-351.
    • (1991) Trans. Am. Math. Soc. , vol.324 , pp. 331-351
    • Novick-Cohen, A.1    Pego, R.L.2
  • 11
    • 0003521975 scopus 로고    scopus 로고
    • 2nd edn, Interdisciplinary Applied Mathematics Series. Heidelberg: Springer
    • Okubo, A. & Levin, S. A. (2001) Diffusion and Ecological Problems 2nd edn, Interdisciplinary Applied Mathematics Series Vol. 14. Heidelberg: Springer.
    • (2001) Diffusion and Ecological Problems , vol.14
    • Okubo, A.1    Levin, S.A.2
  • 12
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blow-up and collapse: The ABC's of generalized taxis in reinforced random walks
    • Othmer, H. G. & Stevens, A. (1997) Aggregation, blow-up and collapse: the ABC's of generalized taxis in reinforced random walks. SIAM J. Appl. Math., 57, 1044-1081.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 13
    • 20444375250 scopus 로고
    • A model for aggregating populations
    • Int. Conf. on Differential Equations. (C. Perelló et al., eds). Singapore: World Scientific
    • Padrón, V. (1993) A model for aggregating populations. Proc. EQUADIFF 91,, Int. Conf. on Differential Equations. Vols 1, 2. (C. Perelló et al., eds). Singapore: World Scientific, pp. 804-809.
    • (1993) Proc. EQUADIFF 91 , vol.1-2 , pp. 804-809
    • Padrón, V.1
  • 14
    • 0006968788 scopus 로고    scopus 로고
    • Sobolev regularization of a nonlinear ill-posed parabolic problem as a model for aggregating populations
    • Padrón, V. (1998) Sobolev regularization of a nonlinear ill-posed parabolic problem as a model for aggregating populations. Commun. Partial Differ. Eqns, 23, 457-486.
    • (1998) Commun. Partial Differ. Eqns. , vol.23 , pp. 457-486
    • Padrón, V.1
  • 15
    • 20444431378 scopus 로고    scopus 로고
    • Aggregation on a nonlinear parabolic functional differential equation
    • Padrón, V. (1998) Aggregation on a nonlinear parabolic functional differential equation. Divulg. Mat., 6, 149-164.
    • (1998) Divulg. Mat. , vol.6 , pp. 149-164
    • Padrón, V.1
  • 16
    • 84867939463 scopus 로고    scopus 로고
    • Localization in lattice and continuum models of reinforced random walks
    • Painter, K. J., Horstmann, D. & Othmer, H. G. (2003) Localization in lattice and continuum models of reinforced random walks. Appl. Math. Lett., 16, 375-381.
    • (2003) Appl. Math. Lett. , vol.16 , pp. 375-381
    • Painter, K.J.1    Horstmann, D.2    Othmer, H.G.3
  • 17
    • 0025465145 scopus 로고
    • Scale space and edge detection using anisotropic diffusion
    • Perona, P. & Malik, J. (1990) Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell., 12, 629-639.
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell. , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 18
    • 0000715275 scopus 로고
    • Sur une équation intégro-differentielle non linéaire issue de la biologie
    • Rascale, M. (1979) Sur une équation intégro-differentielle non linéaire issue de la biologie. J. Differ. Eqns, 32, 420-453.
    • (1979) J. Differ. Eqns , vol.32 , pp. 420-453
    • Rascale, M.1
  • 19
    • 0004168411 scopus 로고    scopus 로고
    • European Consortium for Mathematics in Industry. Stuttgart: Teubner
    • Weickert, J. (1998) Anisotropic Diffusion in Image Processing. European Consortium for Mathematics in Industry. Stuttgart: Teubner.
    • (1998) Anisotropic Diffusion in Image Processing
    • Weickert, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.