메뉴 건너뛰기




Volumn 120, Issue 3-4, 1998, Pages 346-368

Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system

Author keywords

Fronts; Reaction diffusion equations; Stability; Travelling waves

Indexed keywords


EID: 0000156777     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00096-7     Document Type: Article
Times cited : (39)

References (26)
  • 1
    • 36448999535 scopus 로고
    • Instabilities in propagating reaction-diffusion fronts
    • D. Horváth, V. Petrov, S.K. Scott, K. Showalter, Instabilities in propagating reaction-diffusion fronts, J. Chem. Phys. 98 (8) (1993) 6332-6343.
    • (1993) J. Chem. Phys. , vol.98 , Issue.8 , pp. 6332-6343
    • Horváth, D.1    Petrov, V.2    Scott, S.K.3    Showalter, K.4
  • 2
    • 0001778255 scopus 로고
    • The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves
    • J. Billingham, D.J. Needham, The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves, Phil. Trans. R. Soc. London A 334 (1991) 1-24.
    • (1991) Phil. Trans. R. Soc. London A , vol.334 , pp. 1-24
    • Billingham, J.1    Needham, D.J.2
  • 3
    • 0001543307 scopus 로고
    • On the global existence and asymptotic behavior of solutions of reaction-diffusion equations
    • K. Masuda, On the global existence and asymptotic behavior of solutions of reaction-diffusion equations, Hokkaido Math. J. 12 (1983) 360-370.
    • (1983) Hokkaido Math. J. , vol.12 , pp. 360-370
    • Masuda, K.1
  • 4
    • 84972572538 scopus 로고
    • On a result of K. Masuda concerning reaction-diffusion equations
    • A. Haraux, A. Youkana, On a result of K. Masuda concerning reaction-diffusion equations, Tôhoku Math. J. 40 (1988) 159-163.
    • (1988) Tôhoku Math. J. , vol.40 , pp. 159-163
    • Haraux, A.1    Youkana, A.2
  • 5
    • 0030240068 scopus 로고    scopus 로고
    • Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity
    • J. Bricmont, A. Kupiainen, J. Xin, Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity, J. Diff. Eqs. 130 (1996) 9-35.
    • (1996) J. Diff. Eqs. , vol.130 , pp. 9-35
    • Bricmont, J.1    Kupiainen, A.2    Xin, J.3
  • 6
    • 0011460060 scopus 로고
    • Large time asymptotics of solutions to a model combustion system with critical nonlinearity
    • L. Berlyand, J. Xin, Large time asymptotics of solutions to a model combustion system with critical nonlinearity, Nonlinearity 8 (1995) 161-178.
    • (1995) Nonlinearity , vol.8 , pp. 161-178
    • Berlyand, L.1    Xin, J.2
  • 7
    • 0000077249 scopus 로고
    • Nonlinear reaction-diffusion systems
    • W.F. Ames, C. Rogers (Eds.), Academic Press, Boston
    • R.H. Martin, M. Pierre, Nonlinear reaction-diffusion systems, in: W.F. Ames, C. Rogers (Eds.), Nonlinear Equations in the Applied Sciences, Academic Press, Boston, 1992.
    • (1992) Nonlinear Equations in the Applied Sciences
    • Martin, R.H.1    Pierre, M.2
  • 10
    • 6444221633 scopus 로고
    • Front propagation into unstable states. II. Linear versus nonlinear marginal stability and rate of convergence
    • W. van Saarloos, Front propagation into unstable states. II. Linear versus nonlinear marginal stability and rate of convergence, Phys. Rev. A 39 (12) (1989) 6367-6390.
    • (1989) Phys. Rev. A , vol.39 , Issue.12 , pp. 6367-6390
    • Van Saarloos, W.1
  • 12
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusion arising in population genetics
    • D.G. Aronson, H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978) 33-76.
    • (1978) Adv. Math. , vol.30 , pp. 33-76
    • Aronson, D.G.1    Weinberger, H.F.2
  • 13
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • D.H. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976) 312-355.
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.H.1
  • 14
    • 44049118931 scopus 로고
    • On the nonlinear dynamics of travelling fronts
    • K. Kirchgässner, On the nonlinear dynamics of travelling fronts, J. Diff. Eqs. 96 (1992) 256-278.
    • (1992) J. Diff. Eqs. , vol.96 , pp. 256-278
    • Kirchgässner, K.1
  • 15
    • 34249762638 scopus 로고
    • The nonlinear stability of front solutions for parabolic partial differential equations
    • J.-P. Eckmann, C.E. Wayne, The nonlinear stability of front solutions for parabolic partial differential equations, Comm. Math. Phys. 161 (1994) 323-334.
    • (1994) Comm. Math. Phys. , vol.161 , pp. 323-334
    • Eckmann, J.-P.1    Wayne, C.E.2
  • 16
    • 21344495443 scopus 로고
    • Stability of moving fronts in the Ginzburg-Landau equation
    • J. Bricmont, A. Kupiainen, Stability of moving fronts in the Ginzburg-Landau equation, Comm. Math. Phys. 159 (1994) 287-318.
    • (1994) Comm. Math. Phys. , vol.159 , pp. 287-318
    • Bricmont, J.1    Kupiainen, A.2
  • 17
    • 0001171846 scopus 로고
    • Local stability of critical fronts in nonlinear parabolic partial differential equations
    • Th. Gallay, Local stability of critical fronts in nonlinear parabolic partial differential equations, Nonlinearity 7 (1994) 741-764.
    • (1994) Nonlinearity , vol.7 , pp. 741-764
    • Gallay, T.1
  • 18
    • 85083137956 scopus 로고
    • Periodic patterns and travelling fronts for the Ginzburg-Landau equation
    • World Scientific, Singapore
    • Th. Gallay, Periodic patterns and travelling fronts for the Ginzburg-Landau equation, in: IUTAM/ISIMM-Proceedings Nonlinear Waves in Hannover 1994, World Scientific, Singapore, 1995.
    • (1995) IUTAM/ISIMM-Proceedings Nonlinear Waves in Hannover 1994
    • Gallay, T.1
  • 19
    • 0031490679 scopus 로고    scopus 로고
    • Stability of travelling waves for a damped hyperbolic equation
    • Th. Gallay, G. Raugel, Stability of travelling waves for a damped hyperbolic equation, Z. Angew. Math. Phys. 48 (1997) 451-479.
    • (1997) Z. Angew. Math. Phys. , vol.48 , pp. 451-479
    • Gallay, Th.1    Raugel, G.2
  • 20
    • 33646917618 scopus 로고
    • A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
    • E.B. Fabes, D.W. Stroock, A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash, Arch. Rat. Mech. Anal. 96 (1986) 327-338.
    • (1986) Arch. Rat. Mech. Anal. , vol.96 , pp. 327-338
    • Fabes, E.B.1    Stroock, D.W.2
  • 21
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • R.L. Pego, M.I. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys. 164 (1994) 305-349.
    • (1994) Comm. Math. Phys. , vol.164 , pp. 305-349
    • Pego, R.L.1    Weinstein, M.I.2
  • 23
    • 85083134004 scopus 로고    scopus 로고
    • in preparation
    • S. Focant, in preparation.
    • Focant, S.1
  • 24
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • A. Turing, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. London B 237 (1952) 37-72.
    • (1952) Phil. Trans. Roy. Soc. London B , vol.237 , pp. 37-72
    • Turing, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.