메뉴 건너뛰기




Volumn 23, Issue 2, 2011, Pages 365-393

Linear Stability of Traveling Waves in First-Order Hyperbolic PDEs

Author keywords

Asymptotic behavior; Hyperbolic partial differential equations; Linear stability; Partial differential algebraic equations; Resolvent estimates; Traveling waves

Indexed keywords


EID: 79956120901     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-011-9216-3     Document Type: Article
Times cited : (19)

References (27)
  • 4
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • Beyn W.-J.: The numerical computation of connecting orbits in dynamical systems. IMA J. Numer. Anal. 10(3), 379-405 (1990).
    • (1990) IMA J. Numer. Anal. , vol.10 , Issue.3 , pp. 379-405
    • Beyn, W.-J.1
  • 5
    • 0032678491 scopus 로고    scopus 로고
    • Stability of traveling waves: Dichotomies and eigenvalue conditions on finite intervals
    • Beyn W.-J., Lorenz J.: Stability of traveling waves: Dichotomies and eigenvalue conditions on finite intervals. Numer. Funct. Anal. Optim. 20(3-4), 201-244 (1999).
    • (1999) Numer. Funct. Anal. Optim. , vol.20 , Issue.3-4 , pp. 201-244
    • Beyn, W.-J.1    Lorenz, J.2
  • 6
    • 33646408119 scopus 로고    scopus 로고
    • Stability of viscous profiles: Proofs via dichotomies
    • Beyn W.-J., Lorenz J.: Stability of viscous profiles: proofs via dichotomies. J. Dynam. Differ. Equ. 18(1), 141-195 (2006).
    • (2006) J. Dynam. Differ. Equ. , vol.18 , Issue.1 , pp. 141-195
    • Beyn, W.-J.1    Lorenz, J.2
  • 7
    • 3042573558 scopus 로고    scopus 로고
    • Freezing solutions of equivariant evolution equations
    • (electronic)
    • Beyn W.-J., Thümmler V.: Freezing solutions of equivariant evolution equations. SIAM J. Appl. Dyn. Syst., 3(2), 85-116 (2004) (electronic).
    • (2004) SIAM J. Appl. Dyn. Syst. , vol.3 , Issue.2 , pp. 85-116
    • Beyn, W.-J.1    Thümmler, V.2
  • 8
    • 0035646092 scopus 로고    scopus 로고
    • Numerical testing of the stability of viscous shock waves
    • Brin L. Q.: Numerical testing of the stability of viscous shock waves. Math. Comput. 70(235), 1071-1088 (2001).
    • (2001) Math. Comput. , vol.70 , Issue.235 , pp. 1071-1088
    • Brin, L.Q.1
  • 10
    • 0001472248 scopus 로고
    • Nerve axon equations. I. Linear approximations
    • Evans, J. W.: Nerve axon equations. I. Linear approximations. Indiana Univ. Math. J. 21, 877-885 (1971/1972).
    • (1971) Indiana Univ. Math. J , vol.21 , pp. 877-885
    • Evans, J.W.1
  • 11
    • 0001472247 scopus 로고
    • Nerve axon equations. II. Stability at rest
    • Evans, J. W.: Nerve axon equations. II. Stability at rest. Indiana Univ. Math. J. 22, 75-90 (1972/1973).
    • (1972) Indiana Univ. Math. J , vol.22 , pp. 75-90
    • Evans, J.W.1
  • 12
    • 0001472246 scopus 로고
    • Nerve axon equations. III. Stability of the nerve impulse
    • Evans, J. W.: Nerve axon equations. III. Stability of the nerve impulse. Indiana Univ. Math. J., 22, 577-593, (1972/1973).
    • (1972) Indiana Univ. Math. J , vol.22 , pp. 577-593
    • Evans, J.W.1
  • 13
    • 0016578299 scopus 로고
    • Nerve axon equations. IV. The stable and the unstable impulse
    • Evans, J. W.: Nerve axon equations. IV. The stable and the unstable impulse. Indiana Univ. Math. J. 24(12), 1169-1190 (1974/1975).
    • (1974) Indiana Univ. Math. J , vol.24 , Issue.12 , pp. 1169-1190
    • Evans, J.W.1
  • 14
    • 0003686031 scopus 로고
    • New York: Oxford Mathematical Monographs. The Clarendon Press Oxford University Press
    • Goldstein J. A.: Semigroups of Linear Operators and Application. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (1985).
    • (1985) Semigroups of Linear Operators and Application
    • Goldstein, J.A.1
  • 17
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • Hodgkin A. L., Huxley A. F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500-544 (1952).
    • (1952) J. Physiol. , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 19
    • 0028733434 scopus 로고
    • On the convergence of solutions of nonlinear hyperbolic-parabolic systems
    • Kreiss G., Kreiss H.-O., Petersson N. A.: On the convergence of solutions of nonlinear hyperbolic-parabolic systems. SIAM J. Numer. Anal. 31(6), 1577-1604 (1994).
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.6 , pp. 1577-1604
    • Kreiss, G.1    Kreiss, H.-O.2    Petersson, N.A.3
  • 20
    • 85011437005 scopus 로고    scopus 로고
    • Stability for time-dependent differential equations
    • Acta Numer Cambridge University Press, Cambridge
    • Kreiss, H.-O., Lorenz, J.: Stability for time-dependent differential equations. In: Acta numerica, 1998, volume 7 of Acta Numer., pp 203-285. Cambridge University Press, Cambridge (1998).
    • (1998) Acta numerica , vol.7
    • Kreiss, H.-O.1    Lorenz, J.2
  • 21
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • Palmer K. J.: Exponential dichotomies and transversal homoclinic points. J. Differ. Equ. 55(2), 225-256 (1984).
    • (1984) J. Differ. Equ. , vol.55 , Issue.2 , pp. 225-256
    • Palmer, K.J.1
  • 23
    • 0002307123 scopus 로고
    • Qualitative theory of the FitzHugh-Nagumo equations
    • Rauch J., Smoller J.: Qualitative theory of the FitzHugh-Nagumo equations. Adv. Math. 27(1), 12-44 (1978).
    • (1978) Adv. Math. , vol.27 , Issue.1 , pp. 12-44
    • Rauch, J.1    Smoller, J.2
  • 25
    • 79956083597 scopus 로고    scopus 로고
    • Computation and Stability of Patterns in Hyperbolic-Parabolic Systems
    • PhD thesis, Bielefeld University
    • Rottmann-Matthes, J.: Computation and Stability of Patterns in Hyperbolic-Parabolic Systems. Shaker Verlag, Aachen, 2010. PhD thesis, Bielefeld University (2010).
    • (2010) Shaker Verlag, Aachen, 2010
    • Rottmann-Matthes, J.1
  • 27
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • Sattinger D. H.: On the stability of waves of nonlinear parabolic systems. Adv. Math. 22(3), 312-355 (1976).
    • (1976) Adv. Math. , vol.22 , Issue.3 , pp. 312-355
    • Sattinger, D.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.