메뉴 건너뛰기




Volumn 4, Issue 2, 2004, Pages 157-185

Rigorous numerics for dissipative partial differential equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - A computer-assisted proof

Author keywords

Dissipative PDEs; Galerkin projection; Periodic orbit; Rigorous numerics

Indexed keywords

DIFFERENTIAL INCLUSION; FINITE-DIMENSIONAL TOOLS; PERIODIC ORBITS;

EID: 2642531129     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-002-0080-8     Document Type: Article
Times cited : (75)

References (27)
  • 1
    • 0041893159 scopus 로고
    • Functional analysis and Galerkin's method
    • L. Cesari, Functional analysis and Galerkin's method, Michigan Math. J. 11 (1964), 383-414.
    • (1964) Michigan Math. J. , vol.11 , pp. 383-414
    • Cesari, L.1
  • 2
    • 11744315490 scopus 로고
    • Analyticity for the Kuramoto-Sivashinsky equation
    • P. Collet, J.-P. Eckmann, H. Epstein, and J. Stubbe, Analyticity for the Kuramoto-Sivashinsky equation, Phys. D 67 (1993), 321-326.
    • (1993) Phys. D , vol.67 , pp. 321-326
    • Collet, P.1    Eckmann, J.-P.2    Epstein, H.3    Stubbe, J.4
  • 3
    • 0003560987 scopus 로고
    • Monografie Matematyczne, PWN, Warszawa
    • J. Dugundji and A. Granas, Fixed Point Theory, Monografie Matematyczne, Vol. 61, PWN, Warszawa, 1982.
    • (1982) Fixed Point Theory , vol.61
    • Dugundji, J.1    Granas, A.2
  • 4
    • 33746636159 scopus 로고
    • Gevrey class regularity for the solutions of the Navier-Stokes equations
    • C. Foias and R. Temam, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal. 87 (1989), 359-369.
    • (1989) J. Funct. Anal. , vol.87 , pp. 359-369
    • Foias, C.1    Temam, R.2
  • 5
    • 0001201892 scopus 로고    scopus 로고
    • Computer assisted proof of chaos in the Lorenz system
    • Z. Galias and P. Zgliczyński, Computer assisted proof of chaos in the Lorenz system, Phys. D 115 (1998), 165-188.
    • (1998) Phys. D , vol.115 , pp. 165-188
    • Galias, Z.1    Zgliczyński, P.2
  • 7
    • 84876639163 scopus 로고    scopus 로고
    • Galerkin methods and regularity
    • Fields Inst. Commun., American Mathematical Society, Providence, RI, 2002
    • J. K. Hale and G. Raugel, Galerkin methods and regularity, in Differential Equations and Dynamical Systems (Lisbon, 2000), pp. 173-188, Fields Inst. Commun., Vol. 31, American Mathematical Society, Providence, RI, 2002.
    • (2000) Differential Equations and Dynamical Systems , vol.31 , pp. 173-188
    • Hale, J.K.1    Raugel, G.2
  • 8
    • 45949120176 scopus 로고
    • Do numerical orbits of chaotic dynamical processes represent true orbits?
    • S. M. Hammel, J. A. Yorke, and C. Grebogi, Do numerical orbits of chaotic dynamical processes represent true orbits? J. Complexity 3, (1987) 136-145.
    • (1987) J. Complexity , vol.3 , pp. 136-145
    • Hammel, S.M.1    Yorke, J.A.2    Grebogi, C.3
  • 9
    • 84968480383 scopus 로고
    • Numerical orbits of chaotic dynamical processes represent true orbits
    • S. M. Hammel, J. A. Yorke, and C. Grebogi, Numerical orbits of chaotic dynamical processes represent true orbits, Bull. Amer. Math. Soc. 19, (1988), 465-470.
    • (1988) Bull. Amer. Math. Soc. , vol.19 , pp. 465-470
    • Hammel, S.M.1    Yorke, J.A.2    Grebogi, C.3
  • 11
    • 0003146128 scopus 로고
    • Fourier expansions of the solutions of the Navier-Stokes equations and their exponential decay rate
    • Gauthier-Villars, Montrouge
    • H. -O. Kreiss, Fourier expansions of the solutions of the Navier-Stokes equations and their exponential decay rate, in Analyse Mathématique et Applications, pp. 245-262, Gauthier-Villars, Montrouge, 1988.
    • (1988) Analyse Mathématique et Applications , pp. 245-262
    • Kreiss, H.-O.1
  • 12
    • 0000507179 scopus 로고
    • Persistent propagation of concentration waves in dissipative media far from thermal equilibrium
    • Y. Kuramoto and T. Tsuzuki, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progr. Theoret. Phys. 55 (1976), 365.
    • (1976) Progr. Theoret. Phys. , vol.55 , pp. 365
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 14
    • 0002422258 scopus 로고
    • Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems
    • (J. R. Cash and I. Gladwell, eds.), Clarendon Press, Oxford
    • R. J. Lohner, Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems, in Computational Ordinary Differential Equations (J. R. Cash and I. Gladwell, eds.), Clarendon Press, Oxford, 1992.
    • (1992) Computational Ordinary Differential Equations
    • Lohner, R.J.1
  • 16
    • 0012488396 scopus 로고    scopus 로고
    • Set arithmetic and the enclosing problem in dynamics
    • M. Mrozek and P. Zgliczyński, Set arithmetic and the enclosing problem in dynamics, Ann. Polon. Math. (2000), 237-259.
    • (2000) Ann. Polon. Math. , pp. 237-259
    • Mrozek, M.1    Zgliczyński, P.2
  • 18
    • 0017554878 scopus 로고
    • Nonlinear analysis of hydrodynamical instability in laminar flames - 1. Derivation of basic equations
    • G. I. Sivashinsky, Nonlinear analysis of hydrodynamical instability in laminar flames - 1. Derivation of basic equations, Acta Astronom. 4 (1977), 1177-1206.
    • (1977) Acta Astronom. , vol.4 , pp. 1177-1206
    • Sivashinsky, G.I.1
  • 20
    • 0000527735 scopus 로고    scopus 로고
    • Fixed point index for iterations of maps, topological horseshoe and chaos
    • P. Zgliczńiski, Fixed point index for iterations of maps, topological horseshoe and chaos, Topological Methods Nonlinear Anal. 8 (1996), 169-177.
    • (1996) Topological Methods Nonlinear Anal. , vol.8 , pp. 169-177
    • Zgliczńiski, P.1
  • 21
    • 0041540896 scopus 로고    scopus 로고
    • Computer assisted proof of chaos in the Rössler equations and the Hénon map
    • P. Zgliczyński, Computer assisted proof of chaos in the Rössler equations and the Hénon map, Nonlinearity 10 (1997), 243-252.
    • (1997) Nonlinearity , vol.10 , pp. 243-252
    • Zgliczyński, P.1
  • 22
    • 0033264634 scopus 로고    scopus 로고
    • Sharkovskii's theorem for multidimensional perturbations of 1-dim maps
    • P. Zgliczyński, Sharkovskii's theorem for multidimensional perturbations of 1-dim maps, Ergodic Theory Dynamical Systems 19 (1999) 1655-1684.
    • (1999) Ergodic Theory Dynamical Systems , vol.19 , pp. 1655-1684
    • Zgliczyński, P.1
  • 23
    • 2642522471 scopus 로고    scopus 로고
    • Attracting fixed points for the Kuramoto-Sivashinsky equation - A computer assisted proof
    • P. Zgliczyński, Attracting fixed points for the Kuramoto-Sivashinsky equation - A computer assisted proof, SIAM J. Appl. Dynam. Systems 1 (2002), 215-235, http://epubs.siam.org/sambin/dbq/article/40176
    • (2002) SIAM J. Appl. Dynam. Systems , vol.1 , pp. 215-235
    • Zgliczyński, P.1
  • 25
    • 84876643850 scopus 로고    scopus 로고
    • Trapping regions and an ODE-type proof of an existence and uniqueness for Navier-Stokes equations with periodic boundary conditions on the plane
    • to appear
    • P. Zgliczyński, Trapping regions and an ODE-type proof of an existence and uniqueness for Navier-Stokes equations with periodic boundary conditions on the plane, Univ. Iag. Acta Math. (to appear), http://arXiv.org/ abs/math/0103053
    • Univ. Iag. Acta Math.
    • Zgliczyński, P.1
  • 27
    • 0344578972 scopus 로고    scopus 로고
    • Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation
    • P. Zgliczyński and K. Mischaikow, Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation, Found. Comput. Math. 1 (2001), 255-288.
    • (2001) Found. Comput. Math. , vol.1 , pp. 255-288
    • Zgliczyński, P.1    Mischaikow, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.