Non-dissipative System as Limit of a Dissipative One: Comparison of the Asymptotic Regimes

Ricardo P. Silva1
1Department of Mathematics, University of Brasília, Brasília, Brazil

Tóm tắt

Từ khóa


Tài liệu tham khảo

Babin, A.V., Vishik, M.: Attractors of Evolution Equations, Studies in Mathematics and its Applications, vol. 25. North-Holland Publishing Co., Amsterdam (1992)

Brezis, H.: Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Company, Amsterdam (1973)

Bruschi, S.M., Carvalho, A.N., Pimentel, J.: Limiting grow-up behavior for a one-parameter family of dissipative PDEs. Indiana Univ. Math. J. (2018) (to appear)

Carvalho, A.N., Cholewa, J.W., Dlotko, T.: Global attractors for problems with monotone operators. Bollettino dell’Unione Matematica Italiana 2(3), 693–706 (1999)

Carvalho, A.N., Langa, J.A., Robinson, J.C.: Attractors for Infinite-Dimensional Non-autonomous Dynamical Systems, Applied Mathematical Sciences, vol. 182. Springer, Berlin (2012)

Carvalho, A.N., Pimentel, J.: Autonomous and non-autonomous unbounded attractors under perturbations. Proc. R. Soc. Edinb. Sect. A Math. (2018) (to appear)

Carvalho, A.N., Piskarev, S.: A general approximation scheme for attractors of abstract parabolic problems. Numer. Funct. Anal. Optim. 27(7–8), 785–829 (2006)

Hale, J.K.: Asymptotic Behavior of Dissipative Systems. American Mathematical Society, Providence (1988)

Hale, J.K., Raugel, G.: Lower semicontinuity of attractors of gradient systems and applications. Annali di Matematica Pura ed Applicata 154(4), 281–326 (1989)

Hell, J.: Conley index at infinity. Topol. Methods Nonlinear Anal. 42(1), 137–167 (2013)

Henry, D.: Geometric Theory of Semilinear Parabolic Equations Lecture Notes in Mathematics, vol. 840. Springer, Berlin (1981)

Kloeden, P.E., Simsen, J.: Pullback attractors for non-autonomous evolution equations with spatially variable exponents. Commun. Pure Appl. Anal. 13(6), 2543–2557 (2014)

Lindqvist, P.: Stability for the solutions of $${\rm div}(|\nabla u|^{p-2} \nabla u)=f$$ div ( | ∇ u | p - 2 ∇ u ) = f with varying $$p$$ p . J. Math. Anal. Appl. 127, 93–102 (1987)

Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars (1969)

Pimentel, J., Rocha, C.: A permutation related to non-compact global attractors for slowly non-dissipative systems. J. Dyn. Differ. Equ. 28, 1–28 (2016)

Sakaguchi, S.: Coincidence sets in the obstacle problem for the p-harmonic operators. Proc. Am. Math. Soc. 95, 382–386 (1985)

Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, vol. 68. Springer, Berlin (1988)