메뉴 건너뛰기




Volumn 125, Issue 1, 1996, Pages 239-281

Heteroclinic orbits of semilinear parabolic equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030577735     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0031     Document Type: Article
Times cited : (109)

References (42)
  • 1
    • 0002970101 scopus 로고
    • Global existence for semilinear parabolic equations
    • [Ama85] H. AMANN, Global existence for semilinear parabolic equations, J. Reine. Angew. Math. 360 (1985), 47-83.
    • (1985) J. Reine. Angew. Math. , vol.360 , pp. 47-83
    • Amann, H.1
  • 2
    • 33646918069 scopus 로고
    • The dynamics of rotating waves in scalar reaction diffusion equations
    • [AF88] S. ANGENENT AND B. FIEDLER, The dynamics of rotating waves in scalar reaction diffusion equations, Trans. Amer. Math. Soc. 307 (1988), 545-568.
    • (1988) Trans. Amer. Math. Soc. , vol.307 , pp. 545-568
    • Angenent, S.1    Fiedler, B.2
  • 3
    • 0000005962 scopus 로고
    • Stable transition layers in a semilinear boundary value problem
    • [AMPP87] S. ANGENENT, J. MALLET-PARET, AND L. A. PELETIER, Stable transition layers in a semilinear boundary value problem, J. Diff. Eq. 67 (1987), 212-242.
    • (1987) J. Diff. Eq. , vol.67 , pp. 212-242
    • Angenent, S.1    Mallet-Paret, J.2    Peletier, L.A.3
  • 4
    • 0000329412 scopus 로고
    • The Morse-Smale property for a semi-linear parabolic equation
    • [Ang86] S. ANGENENT, The Morse-Smale property for a semi-linear parabolic equation, J. Diff. Eq. 62 (1986), 427-442.
    • (1986) J. Diff. Eq. , vol.62 , pp. 427-442
    • Angenent, S.1
  • 5
    • 84942222028 scopus 로고
    • The zero set of a solution of a parabolic equation
    • [Ang88] S. ANGENENT, The zero set of a solution of a parabolic equation, J. Reine Angew. Math. 390 (1988), 79-96.
    • (1988) J. Reine Angew. Math. , vol.390 , pp. 79-96
    • Angenent, S.1
  • 6
    • 0002626529 scopus 로고
    • 4, hyperbolicity and projective topology
    • 4, hyperbolicity and projective topology, Siberian Math. J. 29 (1988), 717-726.
    • (1988) Siberian Math. J. , vol.29 , pp. 717-726
    • Arnol'd, V.I.1
  • 7
    • 0000605470 scopus 로고
    • Numbers of zeros on invariant manifolds in reaction-diffusion equations
    • [BF86] P. BRUNOVSKÝ AND B. FIEDLER, Numbers of zeros on invariant manifolds in reaction-diffusion equations, Nonlin. Anal. 10 (1986), 179-193.
    • (1986) Nonlin. Anal. , vol.10 , pp. 179-193
    • Brunovský, P.1    Fiedler, B.2
  • 8
    • 0002264165 scopus 로고
    • Connecting orbits in scalar reaction diffusion equations
    • [BF88] P. BRUNOVSKÝ AND B. FIEDLER, Connecting orbits in scalar reaction diffusion equations, Dynamics Reported 1 (1988), 57-89.
    • (1988) Dynamics Reported , vol.1 , pp. 57-89
    • Brunovský, P.1    Fiedler, B.2
  • 9
    • 0001168397 scopus 로고
    • Connecting orbits in scalar reaction diffusion equations II: The complete solution
    • [BF89] P. BRUNOVSKÝ AND B. FIEDLER, Connecting orbits in scalar reaction diffusion equations II: The complete solution, J. Diff. Eq. 81 (1989), 106-135.
    • (1989) J. Diff. Eq. , vol.81 , pp. 106-135
    • Brunovský, P.1    Fiedler, B.2
  • 10
    • 0003266716 scopus 로고
    • Attractors in evolutionary equations
    • North-Holland Publ. Co., Amsterdam
    • [BV92] A. V. BABIN AND M.I. VISHIK, "Attractors in Evolutionary Equations," Stud. Math. Appl. Vol. 25, North-Holland Publ. Co., Amsterdam, 1992.
    • (1992) Stud. Math. Appl. , vol.25
    • Babin, A.V.1    Vishik, M.I.2
  • 11
    • 0016345113 scopus 로고
    • A bifurcation problem for a nonlinear parabolic equation
    • [CI74] N. CHAFEE AND E. INFANTE, A bifurcation problem for a nonlinear parabolic equation, J. Applicable Analysis 4 (1974), 17-37.
    • (1974) J. Applicable Analysis , vol.4 , pp. 17-37
    • Chafee, N.1    Infante, E.2
  • 12
    • 0003262604 scopus 로고
    • Isolated invariant sets and the morse index
    • AMS, Providence, RI
    • [Con78] C. C. CONLEY, "Isolated Invariant Sets and the Morse Index," CBMS Notes Vol. 38, AMS, Providence, RI, 1978.
    • (1978) CBMS Notes , vol.38
    • Conley, C.C.1
  • 13
    • 0001863910 scopus 로고
    • Slow-motion manifolds, dormant instability, and singular perturbations
    • [FH89] G. FUSCO AND J. K. HALE, Slow-motion manifolds, dormant instability, and singular perturbations, J. Dyn. Diff. Eq. 1 (1989), 111-137.
    • (1989) J. Dyn. Diff. Eq. , vol.1 , pp. 111-137
    • Fusco, G.1    Hale, J.K.2
  • 14
    • 0000618948 scopus 로고
    • Discrete Ljapunov functionals and ω-limit sets
    • [Fie89] B. FIEDLER, Discrete Ljapunov functionals and ω-limit sets, Math. Mod. Num. Anal. 23 (1989), 415-431.
    • (1989) Math. Mod. Num. Anal. , vol.23 , pp. 415-431
    • Fiedler, B.1
  • 15
    • 0001794246 scopus 로고
    • Global attractors of one-dimensional parabolic equations: Sixteen examples
    • [Fie94] B. FIEDLER, Global attractors of one-dimensional parabolic equations: sixteen examples, Tatra Mountains Math. Publ. 4 (1994), 67-92.
    • (1994) Tatra Mountains Math. Publ. , vol.4 , pp. 67-92
    • Fiedler, B.1
  • 16
    • 0001330998 scopus 로고
    • The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces
    • [FraM88] R. FRANZOSA AND K. MISCHAIKOW, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces, J. Diff. Eq. 71 (1988), 270-287.
    • (1988) J. Diff. Eq. , vol.71 , pp. 270-287
    • Franzosa, R.1    Mischaikow, K.2
  • 17
    • 21144481251 scopus 로고
    • Dynamics of bifurcations for variational problems with O(3) equivariance: A Conley index approach
    • [FM92] B. FIEDLER AND K. MISCHAIKOW, Dynamics of bifurcations for variational problems with O(3) equivariance: a Conley index approach, Arch. Rational Mech. Analysis 119 (1992), 145-196.
    • (1992) Arch. Rational Mech. Analysis , vol.119 , pp. 145-196
    • Fiedler, B.1    Mischaikow, K.2
  • 18
    • 0000980087 scopus 로고
    • A poincaré-bendixson theorem for scalar reaction diffusion equations
    • [FMP89] B. FIEDLER AND J. MALLET-PARET, A Poincaré-Bendixson theorem for scalar reaction diffusion equations, Arch. Rational Mech. Anal. 107 (1989), 325-345.
    • (1989) Arch. Rational Mech. Anal. , vol.107 , pp. 325-345
    • Fiedler, B.1    Mallet-Paret, J.2
  • 19
    • 0002238002 scopus 로고
    • A permutation related to the dynamics of a scalar parabolic PDE
    • [FR91] G. FUSCO AND C. ROCHA, A permutation related to the dynamics of a scalar parabolic PDE, J. Diff. Eq. 91 (1991), 75-94.
    • (1991) J. Diff. Eq. , vol.91 , pp. 75-94
    • Fusco, G.1    Rocha, C.2
  • 20
    • 84966252851 scopus 로고
    • The connection matrix theory for Morse decompostions
    • [Fra89] R. FRANZOSA, The connection matrix theory for Morse decompostions, Trans. AMS 311 (1989), 781-803.
    • (1989) Trans. AMS , vol.311 , pp. 781-803
    • Franzosa, R.1
  • 21
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • AMS, Providence, RI
    • [Hal88] J. K. HALE, "Asymptotic Behavior of Dissipative Systems," Math. Surv. Vol. 25, AMS, Providence, RI, 1988.
    • (1988) Math. Surv. , vol.25
    • Hale, J.K.1
  • 22
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Verlag, New York
    • [Hen81] D. HENRY, "Geometric Theory of Semilinear Parabolic Equations," Lect. Notes Math. Vol. 840, Springer-Verlag, New York, 1981.
    • (1981) Lect. Notes Math. , vol.840
    • Henry, D.1
  • 23
    • 46549093257 scopus 로고
    • Some infinite dimensional Morse-Smale systems defined by parabolic differential equations
    • [Hen85] D. HENRY, Some infinite dimensional Morse-Smale systems defined by parabolic differential equations, J. Diff. Eq. 59 (1985), 165-205.
    • (1985) J. Diff. Eq. , vol.59 , pp. 165-205
    • Henry, D.1
  • 24
    • 0003258399 scopus 로고
    • An introduction to infinite dimensional dynamical systems - Geometric theory
    • Springer-Verlag, New York
    • [HMO84] J. HALE, L. T. MAGALHÃES, AND W. M. OLIVA, "An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory," Springer Appl. Math. Sciences Vol. 47, Springer-Verlag, New York, 1984.
    • (1984) Springer Appl. Math. Sciences , vol.47
    • Hale, J.1    Magalhães, L.T.2    Oliva, W.M.3
  • 25
    • 0000446574 scopus 로고
    • Existence and stability of transition layers
    • [HS88] J. HALE AND K. SAKAMOTO, Existence and stability of transition layers, Japan J. Appl. Math. 5 (1988), 367-405.
    • (1988) Japan J. Appl. Math. , vol.5 , pp. 367-405
    • Hale, J.1    Sakamoto, K.2
  • 27
    • 0002887375 scopus 로고
    • Qualitative analysis of the periodically forced relaxation oscillations
    • [Lev81] M. LEVI, Qualitative analysis of the periodically forced relaxation oscillations, AMS Memoirs 32 (1981).
    • (1981) AMS Memoirs , vol.32
    • Levi, M.1
  • 29
    • 0000675919 scopus 로고
    • Convergence of solutions of one-dimensional semilinear parabolic equations
    • [Mat78] H. MATANO, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ. 18 (1978), 221-227.
    • (1978) J. Math. Kyoto Univ. , vol.18 , pp. 221-227
    • Matano, H.1
  • 31
    • 0000657925 scopus 로고
    • Nonincrease of the lap-number of a solution for a one-dimensional semi-linear parabolic equation
    • [Mat82] H. MATANO, Nonincrease of the lap-number of a solution for a one-dimensional semi-linear parabolic equation, J. Fac. Sci. Univ. Tokyo Sec. IA 29 (1982), 401-411.
    • (1982) J. Fac. Sci. Univ. Tokyo Sec. IA , vol.29 , pp. 401-411
    • Matano, H.1
  • 32
    • 0011697319 scopus 로고
    • The connection map for attractor-repeller pairs
    • [McC88] C. MCCORD, The connection map for attractor-repeller pairs, Trans. Amer. Math. Soc. 301 (1988), 195-203.
    • (1988) Trans. Amer. Math. Soc. , vol.301 , pp. 195-203
    • McCord, C.1
  • 35
    • 0001328790 scopus 로고
    • Structural stability theorems
    • "Global Analysis," AMS, Providence, RI
    • [PS70] J. PALIS AND S. SMALE, Structural stability theorems, in "Global Analysis," Proc. Symp. in Pure Math, Vol. XIV, AMS, Providence, RI, 1970.
    • (1970) Proc. Symp. in Pure Math , vol.14
    • Palis, J.1    Smale, S.2
  • 36
    • 0001032545 scopus 로고
    • Properties of the attractor of a scalar parabolic PDE
    • [Roc91] C. ROCHA, Properties of the attractor of a scalar parabolic PDE, J. Dyn. Diff. Eq. 3 (1991), 575-591.
    • (1991) J. Dyn. Diff. Eq. , vol.3 , pp. 575-591
    • Rocha, C.1
  • 37
    • 84968469711 scopus 로고
    • On the homotopy index for infinite dimensional semi-flows
    • [Ryb82] K. RYBAKOWSKI, On the homotopy index for infinite dimensional semi-flows, Trans. Amer. Math. Soc. 269 (1982), 351-382.
    • (1982) Trans. Amer. Math. Soc. , vol.269 , pp. 351-382
    • Rybakowski, K.1
  • 38
    • 0003208393 scopus 로고
    • Global solution branches of two point boundary value problems
    • Springer-Verlag, New York
    • [Sch90] R. SCHAAF, "Global Solution Branches of Two Point Boundary Value Problems," Lect. Notes Math., Vol. 1458, Springer-Verlag, New York, 1990.
    • (1990) Lect. Notes Math. , vol.1458
    • Schaaf, R.1
  • 40
    • 0011686983 scopus 로고
    • Stationary and quasi-stationary shock waves for non-spatially homogeneous Burger's equation in the limit of small dissipation, I
    • [Wol92a] G. WOLANSKY, Stationary and quasi-stationary shock waves for non-spatially homogeneous Burger's equation in the limit of small dissipation, I, Indiana Univ. Math. J. 41 (1992), 43-69.
    • (1992) Indiana Univ. Math. J. , vol.41 , pp. 43-69
    • Wolansky, G.1
  • 42
    • 0001883857 scopus 로고
    • Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable
    • [Zel68] T. I. ZELENYAK, Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable, Differential Equations 4 (1968), 17-22.
    • (1968) Differential Equations , vol.4 , pp. 17-22
    • Zelenyak, T.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.