Geodesic
Local center manifold for parabolic equations with infinite delay
Mathematica Bohemica, Tome 119 (1994) no. 3, pp. 285-304

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The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.
The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.
DOI : 10.21136/MB.1994.126163
Classification : 34K15, 34K20, 34K30, 35B35, 35R10, 45K05, 45N05, 47N20
Keywords: parabolic integrodifferential equations; invariant manifolds; functional equations; analytic semigroup; Banach space; resolvent operator; interpolation spaces; center manifold; parabolic functional equation; infinite delay; solution semigroup 
Petzeltová, Hana. Local center manifold for parabolic equations with infinite delay. Mathematica Bohemica, Tome 119 (1994) no. 3, pp. 285-304. doi: 10.21136/MB.1994.126163
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[1] P. Acquistаpаce B. Tereni: Hölder classes with boundaгy conditions as interpolation spaces. Math Z. 195 (1987), 451-471. | MR

[2] G. Dа Prаto A. Lunаrdi: Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space. Arch. Rat. Mech. Anal. 101 (1988), 115-141. | DOI | MR

[3] J. K. Hаle J. Kаto: Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21 (1978), 11-41. | MR

[4] D. Henry: Geometric theory of semilinear parabolic equations. Lecture Notes in Math. 840, Springer Verlag, 1981. | DOI | MR | Zbl

[5] S. O. Londen J. A. Nohel: Nonlinear Volterra integrodifferential equation occuring in heat flow. Ј. Int. Equations 6 (1984), 11-50. | MR

[6] A. Lunаrdi: Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations. Math. Nachr. 121 (1985), 295-318. | DOI | MR

[7] A. Lunаrdi: Stability and local invariant manifolds in fully nonlinear parabolic equations. Preprint. | MR

[8] J. Milotа: Asymptotic behaviour of parabolic equations with infinite delay. Volterra Integrodiff. Eqs. and Appl., Pitman Research Notes in Math. 190 (1989), 295-305. | MR

[9] H. Petzeltová: Solution semigroup and invariant manifolds for functional equations with infìnite delay. Mathematica Bohemica 118 (1993), no. 2, 175-193. | MR

[10] H. Petzeltová J. Milotа: Resolvent operator for abstract functional differential equations with infinite delay. Numer. Funct. Anal. and Optimiz. 9 (1987), 779-807. | DOI

[11] G. Simonett: Zentrumsmannigfaltigkeiten für quasilineare parabolische Gleichungen. Thesis.

[12] E. Sinestrаri: On the abstract Cauchy problem of parabolic type in the spaces of continuous functions. Ј. Math. And Appl. 107(1985), 16-66.

[13] A. Vаnderbаuwhede: Center manifolds, normal forms and elementary bifurcations. Dynamics reported 2 (1989), 89-169. | DOI | MR

[14] A. Vanderbauwhede G. Iooss: Center manifold theory in infìnite dimensions. Dynamics reported 1 (1992), 125-163. | DOI | MR

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