메뉴 건너뛰기




Volumn 250, Issue 3, 2011, Pages 1310-1333

Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis

Author keywords

Chemotaxis; Conservation law; Energy estimates; Keller Segel model; Large amplitude; Nonlinear stability; Traveling waves

Indexed keywords


EID: 78349306274     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2010.09.020     Document Type: Article
Times cited : (106)

References (22)
  • 1
    • 0014013196 scopus 로고
    • Chemotaxis in bacteria
    • Adler J. Chemotaxis in bacteria. Science 1966, 153:708-716.
    • (1966) Science , vol.153 , pp. 708-716
    • Adler, J.1
  • 2
    • 0014692237 scopus 로고
    • Chemoreceptors in bacteria
    • Adler J. Chemoreceptors in bacteria. Science 1969, 166:1588-1597.
    • (1969) Science , vol.166 , pp. 1588-1597
    • Adler, J.1
  • 3
    • 0000268135 scopus 로고
    • The advance of advantageous genes
    • Fisher R.A. The advance of advantageous genes. Ann. Eugenics 1937, 7:355-369.
    • (1937) Ann. Eugenics , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 4
    • 0022865466 scopus 로고
    • Nonlinear asymptotic stability of viscous shock profiles for conservation laws
    • Goodman J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Ration. Mech. Anal. 1986, 95:325-344.
    • (1986) Arch. Ration. Mech. Anal. , vol.95 , pp. 325-344
    • Goodman, J.1
  • 5
    • 0036003028 scopus 로고    scopus 로고
    • Spectral stability of small-amplitude shock profiles for dissipative symmetric hyperbolic-parabolic systems
    • Humpherys J., Zumbrun K. Spectral stability of small-amplitude shock profiles for dissipative symmetric hyperbolic-parabolic systems. Z. Angew. Math. Phys. 2002, 53:20-34.
    • (2002) Z. Angew. Math. Phys. , vol.53 , pp. 20-34
    • Humpherys, J.1    Zumbrun, K.2
  • 6
    • 62449235559 scopus 로고
    • Stability of shock profiles in viscoelasticity with non-convex constitutive relations
    • Kawashima S., Matsumura A. Stability of shock profiles in viscoelasticity with non-convex constitutive relations. Comm. Pure Appl. Math. 1994, 47:1547-1569.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 1547-1569
    • Kawashima, S.1    Matsumura, A.2
  • 7
    • 0015010990 scopus 로고
    • Traveling bands of chemotactic bacteria: a theoretical analysis
    • Keller E.F., Segel L.A. Traveling bands of chemotactic bacteria: a theoretical analysis. J. Theoret. Biol. 1971, 26:235-248.
    • (1971) J. Theoret. Biol. , vol.26 , pp. 235-248
    • Keller, E.F.1    Segel, L.A.2
  • 8
    • 0002722044 scopus 로고
    • A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem
    • Kolmogorov A.N., Petrovskii I.G., Piskunov N.S. A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Bjol. Moskov. Gos. Univ. 1937, 17:1-72.
    • (1937) Bjol. Moskov. Gos. Univ. , vol.17 , pp. 1-72
    • Kolmogorov, A.N.1    Petrovskii, I.G.2    Piskunov, N.S.3
  • 9
    • 84980077727 scopus 로고
    • Hyperbolic systems of conservation laws ii
    • Lax P. Hyperbolic systems of conservation laws ii. Comm. Pure Appl. Math. 1957, 10:537-566.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537-566
    • Lax, P.1
  • 10
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • Levine H.A., Sleeman B.D. A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM J. Appl. Math. 1997, 57:683-730.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 11
    • 67349244630 scopus 로고    scopus 로고
    • Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion
    • Li T. Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion. SIAM J. Math. Anal. 2008, 40:1058-1075.
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 1058-1075
    • Li, T.1
  • 12
    • 73949089999 scopus 로고    scopus 로고
    • Nonlinear stability of traveling waves to a hyperbolic-parabolic system modeling chemotaxis
    • Li T., Wang Z.A. Nonlinear stability of traveling waves to a hyperbolic-parabolic system modeling chemotaxis. SIAM J. Appl. Math. 2009, 70:1522-1541.
    • (2009) SIAM J. Appl. Math. , vol.70 , pp. 1522-1541
    • Li, T.1    Wang, Z.A.2
  • 13
    • 78349311551 scopus 로고    scopus 로고
    • Nonlinear stability of large amplitude viscous shock waves of a generalized hyperbolic-parabolic system arising in chemotaxis
    • in press.
    • T. Li, Z.A. Wang, Nonlinear stability of large amplitude viscous shock waves of a generalized hyperbolic-parabolic system arising in chemotaxis, Math. Models Methods Appl. Sci. 20 (11) (2010), in press. doi:10.1142/S0218202510004830.
    • (2010) Math. Models Methods Appl. Sci. , vol.20 , Issue.11
    • Li, T.1    Wang, Z.A.2
  • 14
    • 0001192857 scopus 로고
    • Nonlinear stability of shock waves for viscous conservation laws
    • Liu T.P. Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 1986, 328:1-108.
    • (1986) Mem. Amer. Math. Soc. , vol.328 , pp. 1-108
    • Liu, T.P.1
  • 15
    • 70349673846 scopus 로고    scopus 로고
    • Time-asymptotic behavior of wave propagation around a viscous shock profile
    • Liu T.P., Zeng Y. Time-asymptotic behavior of wave propagation around a viscous shock profile. Comm. Math. Phys. 2009, 290:23-82.
    • (2009) Comm. Math. Phys. , vol.290 , pp. 23-82
    • Liu, T.P.1    Zeng, Y.2
  • 16
    • 77956173978 scopus 로고    scopus 로고
    • Traveling wave solutions from microscopic to macroscopic chemotaxis models
    • Lui R., Wang Z.A. Traveling wave solutions from microscopic to macroscopic chemotaxis models. J. Math. Biol. 2010, 61:739-761.
    • (2010) J. Math. Biol. , vol.61 , pp. 739-761
    • Lui, R.1    Wang, Z.A.2
  • 17
    • 0001923997 scopus 로고
    • On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas
    • Matsumura A., Nishihara K. On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas. Japan J. Appl. Math. 1985, 2:17-25.
    • (1985) Japan J. Appl. Math. , vol.2 , pp. 17-25
    • Matsumura, A.1    Nishihara, K.2
  • 18
    • 0026305804 scopus 로고
    • Traveling waves in a chemotaxis model
    • Nagai T., Ikeda T. Traveling waves in a chemotaxis model. J. Math. Biol. 1991, 30:169-184.
    • (1991) J. Math. Biol. , vol.30 , pp. 169-184
    • Nagai, T.1    Ikeda, T.2
  • 19
    • 0011400198 scopus 로고
    • Nonlinear Hyperbolic Equations and Related Topics in Fluid Dynamics
    • Département de Mathématique, Université de Paris-Sud, Orsay, France
    • T. Nishida, Nonlinear Hyperbolic Equations and Related Topics in Fluid Dynamics, Publ. Math. D'Orsay 78-02, Département de Mathématique, Université de Paris-Sud, Orsay, France, 1978.
    • (1978) Publ. Math. D'Orsay 78-02
    • Nishida, T.1
  • 20
    • 21144471868 scopus 로고
    • Nonlinear stability of viscous shock waves
    • Szepessy A., Xin Z.P. Nonlinear stability of viscous shock waves. Arch. Ration. Mech. Anal. 1993, 122:53-103.
    • (1993) Arch. Ration. Mech. Anal. , vol.122 , pp. 53-103
    • Szepessy, A.1    Xin, Z.P.2
  • 21
    • 37049029658 scopus 로고    scopus 로고
    • Shock formation in a chemotaxis model
    • Wang Z.A., Hillen T. Shock formation in a chemotaxis model. Math. Methods Appl. Sci. 2008, 31:45-70.
    • (2008) Math. Methods Appl. Sci. , vol.31 , pp. 45-70
    • Wang, Z.A.1    Hillen, T.2
  • 22
    • 11144278473 scopus 로고    scopus 로고
    • Stability of the rarefaction wave for the generalized kdv-burgers equation
    • Wang Z.A., Zhu C.J. Stability of the rarefaction wave for the generalized kdv-burgers equation. Acta Math. Sci. Ser. B Engl. Ed. 2002, 22(3):319-328.
    • (2002) Acta Math. Sci. Ser. B Engl. Ed. , vol.22 , Issue.3 , pp. 319-328
    • Wang, Z.A.1    Zhu, C.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.