Article
MSC:
34K30,
34K99,
35B35,
35B40,
35R10,
45K05,
47D06,
47N20 | MR 1223484 | Zbl 0798.35153 | DOI: 10.21136/MB.1993.126045
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Keywords:
nonlinear diffusion-type equations with infinite delay; existence of stable and unstable manifolds; parabolic functional equation; infinite delay; stable and unstable manifolds
nonlinear diffusion-type equations with infinite delay; existence of stable and unstable manifolds; parabolic functional equation; infinite delay; stable and unstable manifolds
Summary:
It is proved that parabolic equations with infinite delay generate $C_0$-semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
References:
[1] G. Da Prato A. Lunardi: Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space. Arch. Rat. Mech. Anal. 101 (1988), 115-141. DOI 10.1007/BF00251457 | MR 0921935
[2] G. Da Prato A. Lunardi: Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type. Ann. Mat. Pura Appl. 150 (1988), 67-117. DOI 10.1007/BF01761464 | MR 0946030
[3] J. K. Hale J. Kato: Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21 (1978), 11-41. MR 0492721
[4] D. Henry: Geometric theory of semilinear parabolic equations. Lecture Notes in Math., vol. 840, Springer Verlag, 1981. DOI 10.1007/BFb0089647 | MR 0610244 | Zbl 0456.35001
[5] S. O. Londen J. A. Nohel: Nonlinear Volterra integrodifferential equation occuring in heat flow. J. Int. Equations 6(1984), 11-50. MR 0727934
[6] A. Lunardi: 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 10.1002/mana.19851210120 | MR 0809327 | Zbl 0568.47035
[7] A. Lunardi: On the linear heat equation for materials of fading memory type. SIAM J. Math. Anal. 21 (1990), 1213-1224. DOI 10.1137/0521066 | MR 1062400
[8] J. Milota: Asymptotic behaviour of parabolic equations with infinite delay. Volterra Integrodiff. Eqs. and Appl., Pitman Research Notes in Math. 190, 1989, pp. 295-305. MR 1018887
[9] J. Milota: Stability and saddle-point property for a linear autonomous functional parabolic equations. Comm. Math. Univ. Carolinae 27 (1986), 87-101. MR 0843423
[10] H. Petzeltová J. Milota: Resolvent operator for abstract functional differential equations with infinite delay. Numer. Funct. Anal. and Optimiz. 9 (1987), 779-807. DOI 10.1080/01630568708816261 | MR 0910855
[11] E. Sinestrari: On the abstract Cauchy problem of parabolic type in the spaces of continuous functions. J. Math. An. Appl. 107 (1985), 16-66. DOI 10.1016/0022-247X(85)90353-1 | MR 0786012
[12] C. C. Travis G. F. Webb: Existence and stability for partial functional differential equations. TAMS 200 (1974), 395-418. DOI 10.1090/S0002-9947-1974-0382808-3 | MR 0382808
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