메뉴 건너뛰기




Volumn 16, Issue 1-2, 2011, Pages 31-60

Local well posedness and instability of travelling waves in a chemotaxis model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84867860603     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (23)
  • 1
    • 0002709196 scopus 로고
    • Dichotomies in Stability Theory
    • Springer, Berlin
    • W.A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Math. Vol. 629, Springer, Berlin 1978.
    • (1978) Lecture Notes in Math , vol.629
    • Coppel, W.A.1
  • 2
    • 0011659464 scopus 로고
    • Nonlinear Diffusion Problems
    • (Ed.), Mathematical Center Tracts, Amsterdam
    • O. Diekmann and N. M. Temme (Ed.), "Nonlinear Diffusion Problems," Mathematical Center Tracts, Amsterdam 1976.
    • (1976)
    • Diekmann, O.1    Temme, N.M.2
  • 3
    • 3843116761 scopus 로고    scopus 로고
    • Chemotaxis
    • Imperial College Press
    • M. Eisenbach et al., "Chemotaxis," Imperial College Press 2004.
    • (2004)
    • Eisenbach, M.1
  • 4
    • 0003636817 scopus 로고    scopus 로고
    • One-Parameter Semigroups for Linear Evolution Equations
    • Springer Verlag, New York
    • K.-J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Springer Verlag, New York 2000.
    • (2000)
    • Engel, K.-J.1    Nagel, R.2
  • 5
    • 84886549221 scopus 로고    scopus 로고
    • Traveling Front Solutions Arising in a Chemotaxis-growth model
    • M. Funaki, M. Mimura, and T. Tsujikawa, Traveling Front Solutions Arising in a Chemotaxis-growth model, RIMS Kokyuroku, 1134 (2000), 52-76.
    • (2000) RIMS Kokyuroku , vol.1134 , pp. 52-76
    • Funaki, M.1    Mimura, M.2    Tsujikawa, T.3
  • 6
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, New York
    • D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Math., Vol. 840, Springer, New York 1981.
    • (1981) Lecture Notes in Math , vol.840
    • Henry, D.1
  • 7
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel Model in chemotaxis and its consequences I
    • D. Horstmann, From 1970 until present: The Keller-Segel Model in chemotaxis and its consequences I, Jahresbericht DMV, 105 (2003), 103-165.
    • (2003) Jahresbericht DMV , vol.105 , pp. 103-165
    • Horstmann, D.1
  • 8
    • 13844288282 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel Model in chemotaxis and its consequences II
    • D. Horstmann, From 1970 until present: The Keller-Segel Model in chemotaxis and its consequences II, Jahresbericht DMV, 106 (2004), 51-69.
    • (2004) Jahresbericht DMV , vol.106 , pp. 51-69
    • Horstmann, D.1
  • 9
    • 84867943821 scopus 로고    scopus 로고
    • A constructive approach to traveling waves in chemo-taxis
    • D. Horstmann and A. Stevens, A constructive approach to traveling waves in chemo-taxis, J. Nonlinear Sci., 14 (2004), 1-25.
    • (2004) J. Nonlinear Sci. , vol.14 , pp. 1-25
    • Horstmann, D.1    Stevens, A.2
  • 10
    • 0003862232 scopus 로고
    • Perturbation Theory for Linear Operators
    • Springer, New York
    • T. Kato, "Perturbation Theory for Linear Operators," Springer, New York 1966.
    • (1966)
    • Kato, T.1
  • 11
    • 0015010990 scopus 로고
    • Travelling bands of chemotactic bacteria: A theoretical analysis
    • E. F. Keller and L. A. Segel, Travelling bands of chemotactic bacteria: A theoretical analysis, J. Theor. Biology, 30 (1971), 235-248.
    • (1971) J. Theor. Biology , vol.30 , pp. 235-248
    • Keller, E.F.1    Segel, L.A.2
  • 12
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique
    • A. Kolmogoroff, I. Petrovsky, and N. Piscounoff, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Moscow Univ. Bull. Math., 1 (1937), 1-25.
    • (1937) Moscow Univ. Bull. Math. , vol.1 , pp. 1-25
    • Kolmogoroff, A.1    Petrovsky, I.2    Piscounoff, N.3
  • 13
    • 0003963531 scopus 로고
    • Analytic Semigroups and Optimal Regularity in Parabolic Problems
    • Birkhäuser Verlag
    • A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhäuser Verlag 1995.
    • (1995)
    • Lunardi, A.1
  • 14
    • 84893844274 scopus 로고    scopus 로고
    • Nonlinear parabolic equations and systems
    • C. M. Dafermos, E. Feireisl (ed.) Elsevier/North-Holland
    • A. Lunardi, Nonlinear parabolic equations and systems, In: C. M. Dafermos, E. Feireisl (ed.): "Handbook of Differential Equations Vol. 1," Elsevier/North-Holland (2004), 387-436.
    • (2004) Handbook of Differential Equations , vol.1 , pp. 387-436
    • Lunardi, A.1
  • 15
    • 0003677528 scopus 로고
    • Linear Differential Equations and Function Spaces
    • Academic Press, New York
    • J. L. Massera and J. J. Schäffer, "Linear Differential Equations and Function Spaces," Academic Press, New York 1966.
    • (1966)
    • Massera, J.L.1    Schäffer, J.J.2
  • 16
    • 0026305804 scopus 로고
    • Traveling waves in a chemotactic model
    • T. Nagai and T. Ikeda, Traveling waves in a chemotactic model, J. Math. Biol., 30 (1991), 169-184.
    • (1991) J. Math. Biol. , vol.30 , pp. 169-184
    • Nagai, T.1    Ikeda, T.2
  • 17
    • 0002987277 scopus 로고
    • Towards a "Matrix Theory" for unbounded operator matrices
    • R. Nagel, Towards a "Matrix Theory" for unbounded operator matrices, Math. Z., 201 (1989), 57-68.
    • (1989) Math. Z. , vol.201 , pp. 57-68
    • Nagel, R.1
  • 18
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Di. Eq., 55 (1984), 225-256.
    • (1984) J. Di. Eq. , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 19
    • 84968484465 scopus 로고
    • Exponential dichotomies and Fredholm operators
    • K. J. Palmer, Exponential dichotomies and Fredholm operators, Proc. Amer. Math. Soc., 104 (1988), 149-156.
    • (1988) Proc. Amer. Math. Soc. , vol.104 , pp. 149-156
    • Palmer, K.J.1
  • 20
    • 0003698819 scopus 로고    scopus 로고
    • Differential Equations and Dynamical Systems
    • (Second Edition), Texts in Applied Mathematics 7, Springer, New York
    • L. Perko, "Differential Equations and Dynamical Systems," (Second Edition), Texts in Applied Mathematics 7, Springer, New York 1996.
    • (1996)
    • Perko, L.1
  • 21
    • 67649363651 scopus 로고    scopus 로고
    • Stability of Travelling Waves"
    • B. Fiedler (ed.), Amsterdam: Elsevier
    • B. Sandstede, Stability of Travelling Waves, In B. Fiedler (ed.), "Handbook of Dynamical Systems Vol. 2," Amsterdam: Elsevier (2002), 983-1055.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 983-1055
    • Sandstede, B.1
  • 22
    • 41649118430 scopus 로고    scopus 로고
    • Relative Morse Indices, Fredholm Indices, and Group Velocities
    • B. Sandstede and A. Scheel, Relative Morse Indices, Fredholm Indices, and Group Velocities, Discrete Contin. Dyn. Syst. A, 20 (2008), 139-158.
    • (2008) Discrete Contin. Dyn. Syst. A , vol.20 , pp. 139-158
    • Sandstede, B.1    Scheel, A.2
  • 23
    • 84893832721 scopus 로고    scopus 로고
    • Travelling Waves for Chemotaxis-Systems
    • MPI-MIS preprint 19/05
    • H. Schwetlick, "Travelling Waves for Chemotaxis-Systems," MPI-MIS preprint 19/05
    • Schwetlick, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.