Attractors for quasilinear second-order parabolic equations of the general form. (English. Russian original) Zbl 0729.35066
J. Sov. Math. 56, No. 2, 2389-2396 (1991); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 171, 163-173 (1989).
See the review in Zbl 0719.35050.
MSC:
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K10 | Second-order parabolic equations |
Citations:
Zbl 0719.35050References:
| [1] | O. A. Ladyzhenskaya, ”On the dynamical system generated by the Navier-Stokes equations,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,27, 91–115 (1972). · Zbl 0327.35064 |
| [2] | O. A. Ladyzhenskaya, ”On the determination of minimal global attractors for the Navier-Stokes and other partial differential equations,” Usp. Mat. Nauk,42, No. 6, 25–60 (1987). · Zbl 0687.35072 |
| [3] | O. A. Ladyzhenskaya, On the determination of minimal global B-attractors for semigroups generated by initialboundary value problems for nonlinear dissipative partial differential equations. Preprint LOMI, E-3-87, Leningrad (1987). |
| [4] | O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence (1968). |
| [5] | O. A. Ladyzhenskaya and N. N. Ural’tseva, ”A survey of results on the solvability of boundary value problems for uniformly elliptic and parabolic second-order equations having unbounded singularities,” Usp. Mat. Nauk,41, No. 5, 59–83 (1986). |
| [6] | O. A. Ladyzhenskaya, ”On estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,163, 105–128 (1987). · Zbl 0665.58039 |
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